ITP001 Axioms: ITP102_7.ax
%------------------------------------------------------------------------------
% File : ITP102_7 : TPTP v8.2.0. Bugfixed v7.5.0.
% Domain : Interactive Theorem Proving
% Axioms : HOL4 syntactic export, chainy mode
% Version : [BG+19] axioms.
% English :
% Refs : [BG+19] Brown et al. (2019), GRUNGE: A Grand Unified ATP Chall
% : [Gau19] Gauthier (2019), Email to Geoff Sutcliffe
% Source : [BG+19]
% Names : sptree.ax [Gau19]
% : HL4102_7.ax [TPAP]
% Status : Satisfiable
% Syntax : Number of formulae : 579 ( 232 unt; 222 typ; 0 def)
% Number of atoms : 849 ( 630 equ)
% Maximal formula atoms : 29 ( 1 avg)
% Number of connectives : 526 ( 34 ~; 15 |; 239 &)
% ( 73 <=>; 165 =>; 0 <=; 0 <~>)
% Maximal formula depth : 35 ( 6 avg)
% Maximal term depth : 14 ( 2 avg)
% Number of types : 4 ( 3 usr)
% Number of type conns : 189 ( 107 >; 82 *; 0 +; 0 <<)
% Number of predicates : 2 ( 1 usr; 0 prp; 1-2 aty)
% Number of functors : 218 ( 218 usr; 25 con; 0-7 aty)
% Number of variables : 2080 (1827 !; 23 ?;2080 :)
% ( 230 !>; 0 ?*; 0 @-; 0 @+)
% SPC : TF1_SAT_EQU_NAR
% Comments :
% Bugfixes : v7.5.0 - Fixes to the axioms.
%------------------------------------------------------------------------------
tff(tyop_2Eind__type_2Erecspace,type,
tyop_2Eind__type_2Erecspace: $tType > $tType ).
tff(tyop_2Elist_2Elist,type,
tyop_2Elist_2Elist: $tType > $tType ).
tff(tyop_2Emin_2Ebool,type,
tyop_2Emin_2Ebool: $tType ).
tff(tyop_2Emin_2Efun,type,
tyop_2Emin_2Efun: ( $tType * $tType ) > $tType ).
tff(tyop_2Enum_2Enum,type,
tyop_2Enum_2Enum: $tType ).
tff(tyop_2Eone_2Eone,type,
tyop_2Eone_2Eone: $tType ).
tff(tyop_2Eoption_2Eoption,type,
tyop_2Eoption_2Eoption: $tType > $tType ).
tff(tyop_2Epair_2Eprod,type,
tyop_2Epair_2Eprod: ( $tType * $tType ) > $tType ).
tff(tyop_2Esptree_2Espt,type,
tyop_2Esptree_2Espt: $tType > $tType ).
tff(app_2E2,type,
app_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(p,type,
p: tyop_2Emin_2Ebool > $o ).
tff(combin_i_2E0,type,
combin_i_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(combin_k_2E0,type,
combin_k_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(combin_s_2E0,type,
combin_s_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c))) ).
tff(c_2Ebool_2E_21_2E0,type,
c_2Ebool_2E_21_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_21_2E1,type,
c_2Ebool_2E_21_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Earithmetic_2E_2A_2E0,type,
c_2Earithmetic_2E_2A_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2A_2E2,type,
c_2Earithmetic_2E_2A_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2E_2B_2E0,type,
c_2Earithmetic_2E_2B_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2B_2E2,type,
c_2Earithmetic_2E_2B_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Epair_2E_2C_2E0,type,
c_2Epair_2E_2C_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(A_27a,A_27b))) ).
tff(c_2Epair_2E_2C_2E2,type,
c_2Epair_2E_2C_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( A_27a * A_27b ) > tyop_2Epair_2Eprod(A_27a,A_27b) ) ).
tff(c_2Earithmetic_2E_2D_2E0,type,
c_2Earithmetic_2E_2D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2E_2D_2E2,type,
c_2Earithmetic_2E_2D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Ebool_2E_2F_5C_2E0,type,
c_2Ebool_2E_2F_5C_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_2F_5C_2E2,type,
c_2Ebool_2E_2F_5C_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Enum_2E0_2E0,type,
c_2Enum_2E0_2E0: tyop_2Enum_2Enum ).
tff(c_2Eprim__rec_2E_3C_2E0,type,
c_2Eprim__rec_2E_3C_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Eprim__rec_2E_3C_2E2,type,
c_2Eprim__rec_2E_3C_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_2Earithmetic_2E_3C_3D_2E0,type,
c_2Earithmetic_2E_3C_3D_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Earithmetic_2E_3C_3D_2E2,type,
c_2Earithmetic_2E_3C_3D_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Emin_2Ebool ).
tff(c_2Emin_2E_3D_2E0,type,
c_2Emin_2E_3D_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_2E2,type,
c_2Emin_2E_3D_2E2:
!>[A_27a: $tType] : ( ( A_27a * A_27a ) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_3D_3D_3E_2E0,type,
c_2Emin_2E_3D_3D_3E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Emin_2E_3D_3D_3E_2E2,type,
c_2Emin_2E_3D_3D_3E_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2E_3F_2E0,type,
c_2Ebool_2E_3F_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_3F_2E1,type,
c_2Ebool_2E_3F_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Emin_2E_40_2E0,type,
c_2Emin_2E_40_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),A_27a) ).
tff(c_2Emin_2E_40_2E1,type,
c_2Emin_2E_40_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > A_27a ) ).
tff(c_2Elist_2EALL__DISTINCT_2E0,type,
c_2Elist_2EALL__DISTINCT_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Ebool) ).
tff(c_2Elist_2EALL__DISTINCT_2E1,type,
c_2Elist_2EALL__DISTINCT_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Emin_2Ebool ) ).
tff(c_2Ealist_2EALOOKUP_2E0,type,
c_2Ealist_2EALOOKUP_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)),tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))) ).
tff(c_2Ealist_2EALOOKUP_2E2,type,
c_2Ealist_2EALOOKUP_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Elist_2Elist(tyop_2Epair_2Eprod(A_27b,A_27a)) * A_27b ) > tyop_2Eoption_2Eoption(A_27a) ) ).
tff(c_2Elist_2EAPPEND_2E0,type,
c_2Elist_2EAPPEND_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Elist_2EAPPEND_2E2,type,
c_2Elist_2EAPPEND_2E2:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Ebool_2EARB_2E0,type,
c_2Ebool_2EARB_2E0:
!>[A_27a: $tType] : A_27a ).
tff(c_2Earithmetic_2EBIT1_2E0,type,
c_2Earithmetic_2EBIT1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EBIT1_2E1,type,
c_2Earithmetic_2EBIT1_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Earithmetic_2EBIT2_2E0,type,
c_2Earithmetic_2EBIT2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2EBIT2_2E1,type,
c_2Earithmetic_2EBIT2_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Esptree_2EBN_2E0,type,
c_2Esptree_2EBN_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))) ).
tff(c_2Esptree_2EBN_2E2,type,
c_2Esptree_2EBN_2E2:
!>[A_27a: $tType] : ( ( tyop_2Esptree_2Espt(A_27a) * tyop_2Esptree_2Espt(A_27a) ) > tyop_2Esptree_2Espt(A_27a) ) ).
tff(c_2Eind__type_2EBOTTOM_2E0,type,
c_2Eind__type_2EBOTTOM_2E0:
!>[A_27a: $tType] : tyop_2Eind__type_2Erecspace(A_27a) ).
tff(c_2Esptree_2EBS_2E0,type,
c_2Esptree_2EBS_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))) ).
tff(c_2Esptree_2EBS_2E3,type,
c_2Esptree_2EBS_2E3:
!>[A_27a: $tType] : ( ( tyop_2Esptree_2Espt(A_27a) * A_27a * tyop_2Esptree_2Espt(A_27a) ) > tyop_2Esptree_2Espt(A_27a) ) ).
tff(c_2Epred__set_2ECARD_2E0,type,
c_2Epred__set_2ECARD_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Enum_2Enum) ).
tff(c_2Epred__set_2ECARD_2E1,type,
c_2Epred__set_2ECARD_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Enum_2Enum ) ).
tff(c_2Ebool_2ECOND_2E0,type,
c_2Ebool_2ECOND_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,A_27a))) ).
tff(c_2Ebool_2ECOND_2E3,type,
c_2Ebool_2ECOND_2E3:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Ebool * A_27a * A_27a ) > A_27a ) ).
tff(c_2Elist_2ECONS_2E0,type,
c_2Elist_2ECONS_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Elist_2ECONS_2E2,type,
c_2Elist_2ECONS_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Eind__type_2ECONSTR_2E0,type,
c_2Eind__type_2ECONSTR_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a)))) ).
tff(c_2Eind__type_2ECONSTR_2E3,type,
c_2Eind__type_2ECONSTR_2E3:
!>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * A_27a * tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)) ) > tyop_2Eind__type_2Erecspace(A_27a) ) ).
tff(c_2Ebool_2EDATATYPE_2E0,type,
c_2Ebool_2EDATATYPE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2EDATATYPE_2E1,type,
c_2Ebool_2EDATATYPE_2E1:
!>[A_27a: $tType] : ( A_27a > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2EDELETE_2E0,type,
c_2Epred__set_2EDELETE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EDELETE_2E2,type,
c_2Epred__set_2EDELETE_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * A_27a ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Epred__set_2EDIFF_2E0,type,
c_2Epred__set_2EDIFF_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EDIFF_2E2,type,
c_2Epred__set_2EDIFF_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Epred__set_2EDISJOINT_2E0,type,
c_2Epred__set_2EDISJOINT_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2EDISJOINT_2E2,type,
c_2Epred__set_2EDISJOINT_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Earithmetic_2EDIV_2E0,type,
c_2Earithmetic_2EDIV_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Earithmetic_2EDIV_2E2,type,
c_2Earithmetic_2EDIV_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Elist_2EEL_2E0,type,
c_2Elist_2EEL_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a)) ).
tff(c_2Elist_2EEL_2E2,type,
c_2Elist_2EEL_2E2:
!>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Elist_2Elist(A_27a) ) > A_27a ) ).
tff(c_2Epred__set_2EEMPTY_2E0,type,
c_2Epred__set_2EEMPTY_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ).
tff(c_2Earithmetic_2EEVEN_2E0,type,
c_2Earithmetic_2EEVEN_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).
tff(c_2Earithmetic_2EEVEN_2E1,type,
c_2Earithmetic_2EEVEN_2E1: tyop_2Enum_2Enum > tyop_2Emin_2Ebool ).
tff(c_2Ebool_2EF_2E0,type,
c_2Ebool_2EF_2E0: tyop_2Emin_2Ebool ).
tff(c_2Eind__type_2EFCONS_2E0,type,
c_2Eind__type_2EFCONS_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))) ).
tff(c_2Eind__type_2EFCONS_2E2,type,
c_2Eind__type_2EFCONS_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a) ) > tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a) ) ).
tff(c_2Epred__set_2EFINITE_2E0,type,
c_2Epred__set_2EFINITE_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool) ).
tff(c_2Epred__set_2EFINITE_2E1,type,
c_2Epred__set_2EFINITE_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) > tyop_2Emin_2Ebool ) ).
tff(c_2Elist_2EFOLDL_2E0,type,
c_2Elist_2EFOLDL_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))) ).
tff(c_2Elist_2EFOLDL_2E3,type,
c_2Elist_2EFOLDL_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27b)) * A_27b * tyop_2Elist_2Elist(A_27a) ) > A_27b ) ).
tff(c_2Elist_2EFOLDR_2E0,type,
c_2Elist_2EFOLDR_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b))) ).
tff(c_2Elist_2EFOLDR_2E3,type,
c_2Elist_2EFOLDR_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)) * A_27b * tyop_2Elist_2Elist(A_27a) ) > A_27b ) ).
tff(c_2Epair_2EFST_2E0,type,
c_2Epair_2EFST_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27a) ).
tff(c_2Epair_2EFST_2E1,type,
c_2Epair_2EFST_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epair_2Eprod(A_27a,A_27b) > A_27a ) ).
tff(c_2Ecombin_2EI_2E0,type,
c_2Ecombin_2EI_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,A_27a) ).
tff(c_2Ecombin_2EI_2E1,type,
c_2Ecombin_2EI_2E1:
!>[A_27a: $tType] : ( A_27a > A_27a ) ).
tff(c_2Epred__set_2EIMAGE_2E0,type,
c_2Epred__set_2EIMAGE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EIMAGE_2E2,type,
c_2Epred__set_2EIMAGE_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Ebool) ) ).
tff(c_2Ebool_2EIN_2E0,type,
c_2Ebool_2EIN_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2EIN_2E2,type,
c_2Ebool_2EIN_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epred__set_2EINSERT_2E0,type,
c_2Epred__set_2EINSERT_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EINSERT_2E2,type,
c_2Epred__set_2EINSERT_2E2:
!>[A_27a: $tType] : ( ( A_27a * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Epred__set_2EINTER_2E0,type,
c_2Epred__set_2EINTER_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EINTER_2E2,type,
c_2Epred__set_2EINTER_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Ecombin_2EK_2E0,type,
c_2Ecombin_2EK_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27a)) ).
tff(c_2Ecombin_2EK_2E1,type,
c_2Ecombin_2EK_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( A_27a > tyop_2Emin_2Efun(A_27b,A_27a) ) ).
tff(c_2Elist_2ELENGTH_2E0,type,
c_2Elist_2ELENGTH_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum) ).
tff(c_2Elist_2ELENGTH_2E1,type,
c_2Elist_2ELENGTH_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Enum_2Enum ) ).
tff(c_2Ebool_2ELET_2E0,type,
c_2Ebool_2ELET_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) ).
tff(c_2Ebool_2ELET_2E2,type,
c_2Ebool_2ELET_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * A_27a ) > A_27b ) ).
tff(c_2Elist_2ELIST__TO__SET_2E0,type,
c_2Elist_2ELIST__TO__SET_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) ).
tff(c_2Elist_2ELIST__TO__SET_2E1,type,
c_2Elist_2ELIST__TO__SET_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Esptree_2ELN_2E0,type,
c_2Esptree_2ELN_2E0:
!>[A_27a: $tType] : tyop_2Esptree_2Espt(A_27a) ).
tff(c_2Esptree_2ELS_2E0,type,
c_2Esptree_2ELS_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)) ).
tff(c_2Esptree_2ELS_2E1,type,
c_2Esptree_2ELS_2E1:
!>[A_27a: $tType] : ( A_27a > tyop_2Esptree_2Espt(A_27a) ) ).
tff(c_2Elist_2EMAP_2E0,type,
c_2Elist_2EMAP_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b))) ).
tff(c_2Elist_2EMAP_2E2,type,
c_2Elist_2EMAP_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Elist_2Elist(A_27a) ) > tyop_2Elist_2Elist(A_27b) ) ).
tff(c_2Elist_2ENIL_2E0,type,
c_2Elist_2ENIL_2E0:
!>[A_27a: $tType] : tyop_2Elist_2Elist(A_27a) ).
tff(c_2Eoption_2ENONE_2E0,type,
c_2Eoption_2ENONE_2E0:
!>[A_27a: $tType] : tyop_2Eoption_2Eoption(A_27a) ).
tff(c_2Earithmetic_2ENUMERAL_2E0,type,
c_2Earithmetic_2ENUMERAL_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Earithmetic_2ENUMERAL_2E1,type,
c_2Earithmetic_2ENUMERAL_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Eoption_2EOPTION__MAP_2E0,type,
c_2Eoption_2EOPTION__MAP_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b))) ).
tff(c_2Eoption_2EOPTION__MAP_2E2,type,
c_2Eoption_2EOPTION__MAP_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Eoption_2Eoption(A_27a) ) > tyop_2Eoption_2Eoption(A_27b) ) ).
tff(c_2Epair_2ESND_2E0,type,
c_2Epair_2ESND_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27b) ).
tff(c_2Epair_2ESND_2E1,type,
c_2Epair_2ESND_2E1:
!>[A_27a: $tType,A_27b: $tType] : ( tyop_2Epair_2Eprod(A_27a,A_27b) > A_27b ) ).
tff(c_2Eoption_2ESOME_2E0,type,
c_2Eoption_2ESOME_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)) ).
tff(c_2Eoption_2ESOME_2E1,type,
c_2Eoption_2ESOME_2E1:
!>[A_27a: $tType] : ( A_27a > tyop_2Eoption_2Eoption(A_27a) ) ).
tff(c_2Epred__set_2ESUBSET_2E0,type,
c_2Epred__set_2ESUBSET_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2ESUBSET_2E2,type,
c_2Epred__set_2ESUBSET_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Enum_2ESUC_2E0,type,
c_2Enum_2ESUC_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Enum_2ESUC_2E1,type,
c_2Enum_2ESUC_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Ebool_2ET_2E0,type,
c_2Ebool_2ET_2E0: tyop_2Emin_2Ebool ).
tff(c_2Ebool_2ETYPE__DEFINITION_2E0,type,
c_2Ebool_2ETYPE__DEFINITION_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2ETYPE__DEFINITION_2E2,type,
c_2Ebool_2ETYPE__DEFINITION_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27b,A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Epair_2EUNCURRY_2E0,type,
c_2Epair_2EUNCURRY_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c)) ).
tff(c_2Epair_2EUNCURRY_2E1,type,
c_2Epair_2EUNCURRY_2E1:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)) > tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27a,A_27b),A_27c) ) ).
tff(c_2Epred__set_2EUNION_2E0,type,
c_2Epred__set_2EUNION_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))) ).
tff(c_2Epred__set_2EUNION_2E2,type,
c_2Epred__set_2EUNION_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) > tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) ) ).
tff(c_2Erelation_2EWF_2E0,type,
c_2Erelation_2EWF_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool) ).
tff(c_2Erelation_2EWF_2E1,type,
c_2Erelation_2EWF_2E1:
!>[A_27a: $tType] : ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) > tyop_2Emin_2Ebool ) ).
tff(c_2Erelation_2EWFREC_2E0,type,
c_2Erelation_2EWFREC_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(A_27a,A_27b))) ).
tff(c_2Erelation_2EWFREC_2E2,type,
c_2Erelation_2EWFREC_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)) * tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27b)) ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).
tff(c_2Earithmetic_2EZERO_2E0,type,
c_2Earithmetic_2EZERO_2E0: tyop_2Enum_2Enum ).
tff(c_2Ebool_2E_5C_2F_2E0,type,
c_2Ebool_2E_5C_2F_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)) ).
tff(c_2Ebool_2E_5C_2F_2E2,type,
c_2Ebool_2E_5C_2F_2E2: ( tyop_2Emin_2Ebool * tyop_2Emin_2Ebool ) > tyop_2Emin_2Ebool ).
tff(c_2Epred__set_2Ecount_2E0,type,
c_2Epred__set_2Ecount_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Epred__set_2Ecount_2E1,type,
c_2Epred__set_2Ecount_2E1: tyop_2Enum_2Enum > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ).
tff(c_2Esptree_2Edelete_2E0,type,
c_2Esptree_2Edelete_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))) ).
tff(c_2Esptree_2Edelete_2E2,type,
c_2Esptree_2Edelete_2E2:
!>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Esptree_2Espt(A_27a) ) > tyop_2Esptree_2Espt(A_27a) ) ).
tff(c_2Esptree_2Edifference_2E0,type,
c_2Esptree_2Edifference_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))) ).
tff(c_2Esptree_2Edifference_2E2,type,
c_2Esptree_2Edifference_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Esptree_2Espt(A_27a) * tyop_2Esptree_2Espt(A_27b) ) > tyop_2Esptree_2Espt(A_27a) ) ).
tff(c_2Esptree_2Edomain_2E0,type,
c_2Esptree_2Edomain_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)) ).
tff(c_2Esptree_2Edomain_2E1,type,
c_2Esptree_2Edomain_2E1:
!>[A_27a: $tType] : ( tyop_2Esptree_2Espt(A_27a) > tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool) ) ).
tff(c_2Esptree_2Efilter__v_2E0,type,
c_2Esptree_2Efilter__v_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))) ).
tff(c_2Esptree_2Efilter__v_2E2,type,
c_2Esptree_2Efilter__v_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool) * tyop_2Esptree_2Espt(A_27a) ) > tyop_2Esptree_2Espt(A_27a) ) ).
tff(c_2Esptree_2Efoldi_2E0,type,
c_2Esptree_2Efoldi_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),A_27a)))) ).
tff(c_2Esptree_2Efoldi_2E3,type,
c_2Esptree_2Efoldi_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))) * tyop_2Enum_2Enum * A_27a ) > tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),A_27a) ) ).
tff(c_2Esptree_2Efoldi_2E4,type,
c_2Esptree_2Efoldi_2E4:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))) * tyop_2Enum_2Enum * A_27a * tyop_2Esptree_2Espt(A_27b) ) > A_27a ) ).
tff(c_2Esptree_2EfromAList_2E0,type,
c_2Esptree_2EfromAList_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)) ).
tff(c_2Esptree_2EfromAList_2E1,type,
c_2Esptree_2EfromAList_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)) > tyop_2Esptree_2Espt(A_27a) ) ).
tff(c_2Esptree_2EfromList_2E0,type,
c_2Esptree_2EfromList_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Esptree_2Espt(A_27a)) ).
tff(c_2Esptree_2EfromList_2E1,type,
c_2Esptree_2EfromList_2E1:
!>[A_27a: $tType] : ( tyop_2Elist_2Elist(A_27a) > tyop_2Esptree_2Espt(A_27a) ) ).
tff(c_2Esptree_2Einsert_2E0,type,
c_2Esptree_2Einsert_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))) ).
tff(c_2Esptree_2Einsert_2E3,type,
c_2Esptree_2Einsert_2E3:
!>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * A_27a * tyop_2Esptree_2Espt(A_27a) ) > tyop_2Esptree_2Espt(A_27a) ) ).
tff(c_2Esptree_2Einter_2E0,type,
c_2Esptree_2Einter_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))) ).
tff(c_2Esptree_2Einter_2E2,type,
c_2Esptree_2Einter_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Esptree_2Espt(A_27a) * tyop_2Esptree_2Espt(A_27b) ) > tyop_2Esptree_2Espt(A_27a) ) ).
tff(c_2Esptree_2Einter__eq_2E0,type,
c_2Esptree_2Einter__eq_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))) ).
tff(c_2Esptree_2Einter__eq_2E2,type,
c_2Esptree_2Einter__eq_2E2:
!>[A_27a: $tType] : ( ( tyop_2Esptree_2Espt(A_27a) * tyop_2Esptree_2Espt(A_27a) ) > tyop_2Esptree_2Espt(A_27a) ) ).
tff(c_2Elist_2Elist__CASE_2E0,type,
c_2Elist_2Elist__CASE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)),A_27b))) ).
tff(c_2Elist_2Elist__CASE_2E3,type,
c_2Elist_2Elist__CASE_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * A_27b * tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27b)) ) > A_27b ) ).
tff(c_2Esptree_2Elist__insert_2E0,type,
c_2Esptree_2Elist__insert_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone))) ).
tff(c_2Esptree_2Elist__insert_2E2,type,
c_2Esptree_2Elist__insert_2E2: ( tyop_2Elist_2Elist(tyop_2Enum_2Enum) * tyop_2Esptree_2Espt(tyop_2Eone_2Eone) ) > tyop_2Esptree_2Espt(tyop_2Eone_2Eone) ).
tff(c_2Esptree_2Elist__to__num__set_2E0,type,
c_2Esptree_2Elist__to__num__set_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Esptree_2Espt(tyop_2Eone_2Eone)) ).
tff(c_2Esptree_2Elist__to__num__set_2E1,type,
c_2Esptree_2Elist__to__num__set_2E1: tyop_2Elist_2Elist(tyop_2Enum_2Enum) > tyop_2Esptree_2Espt(tyop_2Eone_2Eone) ).
tff(c_2Esptree_2Elookup_2E0,type,
c_2Esptree_2Elookup_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a))) ).
tff(c_2Esptree_2Elookup_2E2,type,
c_2Esptree_2Elookup_2E2:
!>[A_27a: $tType] : ( ( tyop_2Enum_2Enum * tyop_2Esptree_2Espt(A_27a) ) > tyop_2Eoption_2Eoption(A_27a) ) ).
tff(c_2Esptree_2Elrnext_2E0,type,
c_2Esptree_2Elrnext_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum) ).
tff(c_2Esptree_2Elrnext_2E1,type,
c_2Esptree_2Elrnext_2E1: tyop_2Enum_2Enum > tyop_2Enum_2Enum ).
tff(c_2Esptree_2Emap_2E0,type,
c_2Esptree_2Emap_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))) ).
tff(c_2Esptree_2Emap_2E2,type,
c_2Esptree_2Emap_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27b,A_27a) * tyop_2Esptree_2Espt(A_27b) ) > tyop_2Esptree_2Espt(A_27a) ) ).
tff(c_2Esptree_2Emapi_2E0,type,
c_2Esptree_2Emapi_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))) ).
tff(c_2Esptree_2Emapi_2E2,type,
c_2Esptree_2Emapi_2E2:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)) * tyop_2Esptree_2Espt(A_27b) ) > tyop_2Esptree_2Espt(A_27a) ) ).
tff(c_2Esptree_2Emapi0_2E0,type,
c_2Esptree_2Emapi0_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))) ).
tff(c_2Esptree_2Emapi0_2E3,type,
c_2Esptree_2Emapi0_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)) * tyop_2Enum_2Enum * tyop_2Esptree_2Espt(A_27b) ) > tyop_2Esptree_2Espt(A_27a) ) ).
tff(c_2Esptree_2Emk__BN_2E0,type,
c_2Esptree_2Emk__BN_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))) ).
tff(c_2Esptree_2Emk__BN_2E2,type,
c_2Esptree_2Emk__BN_2E2:
!>[A_27a: $tType] : ( ( tyop_2Esptree_2Espt(A_27a) * tyop_2Esptree_2Espt(A_27a) ) > tyop_2Esptree_2Espt(A_27a) ) ).
tff(c_2Esptree_2Emk__BS_2E0,type,
c_2Esptree_2Emk__BS_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))) ).
tff(c_2Esptree_2Emk__BS_2E3,type,
c_2Esptree_2Emk__BS_2E3:
!>[A_27a: $tType] : ( ( tyop_2Esptree_2Espt(A_27a) * A_27a * tyop_2Esptree_2Espt(A_27a) ) > tyop_2Esptree_2Espt(A_27a) ) ).
tff(c_2Esptree_2Emk__wf_2E0,type,
c_2Esptree_2Emk__wf_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)) ).
tff(c_2Esptree_2Emk__wf_2E1,type,
c_2Esptree_2Emk__wf_2E1:
!>[A_27a: $tType] : ( tyop_2Esptree_2Espt(A_27a) > tyop_2Esptree_2Espt(A_27a) ) ).
tff(c_2Ecombin_2Eo_2E0,type,
c_2Ecombin_2Eo_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(A_27a,A_27b))) ).
tff(c_2Ecombin_2Eo_2E2,type,
c_2Ecombin_2Eo_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Emin_2Efun(A_27c,A_27b) * tyop_2Emin_2Efun(A_27a,A_27c) ) > tyop_2Emin_2Efun(A_27a,A_27b) ) ).
tff(c_2Eone_2Eone_2E0,type,
c_2Eone_2Eone_2E0: tyop_2Eone_2Eone ).
tff(c_2Eoption_2Eoption__CASE_2E0,type,
c_2Eoption_2Eoption__CASE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),A_27b))) ).
tff(c_2Eoption_2Eoption__CASE_2E3,type,
c_2Eoption_2Eoption__CASE_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Eoption_2Eoption(A_27a) * A_27b * tyop_2Emin_2Efun(A_27a,A_27b) ) > A_27b ) ).
tff(c_2Epair_2Epair__CASE_2E0,type,
c_2Epair_2Epair__CASE_2E0:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : tyop_2Emin_2Efun(tyop_2Epair_2Eprod(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)),A_27a)) ).
tff(c_2Epair_2Epair__CASE_2E2,type,
c_2Epair_2Epair__CASE_2E2:
!>[A_27a: $tType,A_27b: $tType,A_27c: $tType] : ( ( tyop_2Epair_2Eprod(A_27b,A_27c) * tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27c,A_27a)) ) > A_27a ) ).
tff(c_2Esptree_2Esize_2E0,type,
c_2Esptree_2Esize_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Enum_2Enum) ).
tff(c_2Esptree_2Esize_2E1,type,
c_2Esptree_2Esize_2E1:
!>[A_27a: $tType] : ( tyop_2Esptree_2Espt(A_27a) > tyop_2Enum_2Enum ) ).
tff(c_2Esptree_2Espt__CASE_2E0,type,
c_2Esptree_2Espt__CASE_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b))),A_27b))))) ).
tff(c_2Esptree_2Espt__CASE_2E5,type,
c_2Esptree_2Espt__CASE_2E5:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Esptree_2Espt(A_27a) * A_27b * tyop_2Emin_2Efun(A_27a,A_27b) * tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)) * tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b))) ) > A_27b ) ).
tff(c_2Esptree_2Espt__acc_2E0,type,
c_2Esptree_2Espt__acc_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)) ).
tff(c_2Esptree_2Espt__acc_2E2,type,
c_2Esptree_2Espt__acc_2E2: ( tyop_2Enum_2Enum * tyop_2Enum_2Enum ) > tyop_2Enum_2Enum ).
tff(c_2Esptree_2Espt__center_2E0,type,
c_2Esptree_2Espt__center_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)) ).
tff(c_2Esptree_2Espt__center_2E1,type,
c_2Esptree_2Espt__center_2E1:
!>[A_27a: $tType] : ( tyop_2Esptree_2Espt(A_27a) > tyop_2Eoption_2Eoption(A_27a) ) ).
tff(c_2Esptree_2Espt__fold_2E0,type,
c_2Esptree_2Espt__fold_2E0:
!>[A_27a: $tType,A_27b: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),A_27a))) ).
tff(c_2Esptree_2Espt__fold_2E3,type,
c_2Esptree_2Espt__fold_2E3:
!>[A_27a: $tType,A_27b: $tType] : ( ( tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)) * A_27a * tyop_2Esptree_2Espt(A_27b) ) > A_27a ) ).
tff(c_2Esptree_2Espt__left_2E0,type,
c_2Esptree_2Espt__left_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)) ).
tff(c_2Esptree_2Espt__left_2E1,type,
c_2Esptree_2Espt__left_2E1:
!>[A_27a: $tType] : ( tyop_2Esptree_2Espt(A_27a) > tyop_2Esptree_2Espt(A_27a) ) ).
tff(c_2Esptree_2Espt__right_2E0,type,
c_2Esptree_2Espt__right_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)) ).
tff(c_2Esptree_2Espt__right_2E1,type,
c_2Esptree_2Espt__right_2E1:
!>[A_27a: $tType] : ( tyop_2Esptree_2Espt(A_27a) > tyop_2Esptree_2Espt(A_27a) ) ).
tff(c_2Esptree_2Espt__size_2E0,type,
c_2Esptree_2Espt__size_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Enum_2Enum)) ).
tff(c_2Esptree_2Espt__size_2E2,type,
c_2Esptree_2Espt__size_2E2:
!>[A_27a: $tType] : ( ( tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum) * tyop_2Esptree_2Espt(A_27a) ) > tyop_2Enum_2Enum ) ).
tff(c_2Esptree_2Esubspt_2E0,type,
c_2Esptree_2Esubspt_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)) ).
tff(c_2Esptree_2Esubspt_2E2,type,
c_2Esptree_2Esubspt_2E2:
!>[A_27a: $tType] : ( ( tyop_2Esptree_2Espt(A_27a) * tyop_2Esptree_2Espt(A_27a) ) > tyop_2Emin_2Ebool ) ).
tff(c_2Esptree_2EtoAList_2E0,type,
c_2Esptree_2EtoAList_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))) ).
tff(c_2Esptree_2EtoAList_2E1,type,
c_2Esptree_2EtoAList_2E1:
!>[A_27a: $tType] : ( tyop_2Esptree_2Espt(A_27a) > tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)) ) ).
tff(c_2Esptree_2EtoList_2E0,type,
c_2Esptree_2EtoList_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(A_27a)) ).
tff(c_2Esptree_2EtoList_2E1,type,
c_2Esptree_2EtoList_2E1:
!>[A_27a: $tType] : ( tyop_2Esptree_2Espt(A_27a) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Esptree_2EtoListA_2E0,type,
c_2Esptree_2EtoListA_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(A_27a))) ).
tff(c_2Esptree_2EtoListA_2E2,type,
c_2Esptree_2EtoListA_2E2:
!>[A_27a: $tType] : ( ( tyop_2Elist_2Elist(A_27a) * tyop_2Esptree_2Espt(A_27a) ) > tyop_2Elist_2Elist(A_27a) ) ).
tff(c_2Esptree_2Eunion_2E0,type,
c_2Esptree_2Eunion_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))) ).
tff(c_2Esptree_2Eunion_2E2,type,
c_2Esptree_2Eunion_2E2:
!>[A_27a: $tType] : ( ( tyop_2Esptree_2Espt(A_27a) * tyop_2Esptree_2Espt(A_27a) ) > tyop_2Esptree_2Espt(A_27a) ) ).
tff(c_2Esptree_2Ewf_2E0,type,
c_2Esptree_2Ewf_2E0:
!>[A_27a: $tType] : tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool) ).
tff(c_2Esptree_2Ewf_2E1,type,
c_2Esptree_2Ewf_2E1:
!>[A_27a: $tType] : ( tyop_2Esptree_2Espt(A_27a) > tyop_2Emin_2Ebool ) ).
tff(c_2Ebool_2E_7E_2E0,type,
c_2Ebool_2E_7E_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool) ).
tff(c_2Ebool_2E_7E_2E1,type,
c_2Ebool_2E_7E_2E1: tyop_2Emin_2Ebool > tyop_2Emin_2Ebool ).
tff(thm_2Eextra_2Dho_2Eeq__ext,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ! [V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27b,V0f_2E0,V2x_2E0) = app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0) )
=> ( V0f_2E0 = V1g_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Eboolext,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( ( p(V0_2E0)
<=> p(V1_2E0) )
=> ( V0_2E0 = V1_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Etruth,axiom,
p(c_2Ebool_2ET_2E0) ).
tff(thm_2Eextra_2Dho_2Enotfalse,axiom,
~ p(c_2Ebool_2EF_2E0) ).
tff(thm_2Eextra_2Dho_2Ebool__cases__ax,axiom,
! [V0t_2E0: tyop_2Emin_2Ebool] :
( ( V0t_2E0 = c_2Ebool_2ET_2E0 )
| ( V0t_2E0 = c_2Ebool_2EF_2E0 ) ) ).
tff(thm_2Eextra_2Dho_2Ei__thm,axiom,
! [A_27a: $tType,V0x_2E0: A_27a] : ( app_2E2(A_27a,A_27a,combin_i_2E0(A_27a),V0x_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Ek__thm,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27a,V1y_2E0: A_27b] : ( app_2E2(A_27b,A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27a),combin_k_2E0(A_27a,A_27b),V0x_2E0),V1y_2E0) = V0x_2E0 ) ).
tff(thm_2Eextra_2Dho_2Es__thm,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),V1g_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2x_2E0: A_27a] : ( app_2E2(A_27a,A_27c,app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27c)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),combin_s_2E0(A_27a,A_27b,A_27c),V0f_2E0),V1g_2E0),V2x_2E0) = app_2E2(A_27b,A_27c,app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,A_27c),V0f_2E0,V2x_2E0),app_2E2(A_27a,A_27b,V1g_2E0,V2x_2E0)) ) ).
tff(logicdef_2E_2F_5C,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_2F_5C_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
& p(V1_2E0) ) ) ).
tff(logicdef_2E_5C_2F,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_5C_2F_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
| p(V1_2E0) ) ) ).
tff(logicdef_2E_7E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool] :
( p(c_2Ebool_2E_7E_2E1(V0_2E0))
<=> ~ p(V0_2E0) ) ).
tff(logicdef_2E_3D_3D_3E,axiom,
! [V0_2E0: tyop_2Emin_2Ebool,V1_2E0: tyop_2Emin_2Ebool] :
( p(c_2Emin_2E_3D_3D_3E_2E2(V0_2E0,V1_2E0))
<=> ( p(V0_2E0)
=> p(V1_2E0) ) ) ).
tff(logicdef_2E_3D,axiom,
! [A_27a: $tType,V0_2E0: A_27a,V1_2E0: A_27a] :
( p(c_2Emin_2E_3D_2E2(A_27a,V0_2E0,V1_2E0))
<=> ( V0_2E0 = V1_2E0 ) ) ).
tff(quantdef_2E_21,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_21_2E1(A_27a,V0f_2E0))
<=> ! [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(quantdef_2E_3F,axiom,
! [A_27a: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Ebool_2E_3F_2E1(A_27a,V0f_2E0))
<=> ? [V1x_2E0: A_27a] : p(app_2E2(A_27a,tyop_2Emin_2Ebool,V0f_2E0,V1x_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_21_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_21_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_21_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_2A_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2A_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2A_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_2B_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2B_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2B_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: A_27a] : ( c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,A_27a,X0_2E0,X1_2E0) = app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Epair_2E_2C_2E0(tyop_2Enum_2Enum,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))),c_2Epair_2E_2C_2E0(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2E_2C_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27a),X1_2E0: tyop_2Eoption_2Eoption(A_27b)] : ( c_2Epair_2E_2C_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b))),c_2Epair_2E_2C_2E0(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_2D_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_2D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2E_2D_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_2F_5C_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
& p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_2F_5C_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Eprim__rec_2E_3C_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Eprim__rec_2E_3C_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Eprim__rec_2E_3C_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2E_3C_3D_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2E_3C_3D_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Earithmetic_2E_3C_3D_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: A_27a] :
( ( X0_2E0 = X1_2E0 )
<=> p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Emin_2E_3D_2E0(A_27a),X0_2E0),X1_2E0)) ) ).
tff(arityeq2_2Ec_2Emin_2E_3D_3D_3E_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
=> p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Emin_2E_3D_3D_3E_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Ebool_2E_3F_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2E_3F_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Ebool_2E_3F_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_29_2Ctyop_2Emin_2Efun_28tyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E0(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool))),X0_2E0) ) ).
tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E0(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),X0_2E0) ) ).
tff(arityeq1_2Ec_2Emin_2E_40_2E1_2Emono_2Etyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28A_27a_29_2Ctyop_2Emin_2Efun_28tyop_2Esptree_2Espt_28A_27a_29_2Ctyop_2Emin_2Ebool_29_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] : ( c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),c_2Emin_2E_40_2E0(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool))),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2EALL__DISTINCT_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2EALL__DISTINCT_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Ebool,c_2Elist_2EALL__DISTINCT_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ealist_2EALOOKUP_2E2_2Emono_2EA_27a_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X1_2E0: tyop_2Enum_2Enum] : ( c_2Ealist_2EALOOKUP_2E2(A_27a,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eoption_2Eoption(A_27a)),c_2Ealist_2EALOOKUP_2E0(A_27a,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EAPPEND_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2EAPPEND_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2EAPPEND_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),c_2Elist_2EAPPEND_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EAPPEND_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))] : ( c_2Elist_2EAPPEND_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),c_2Elist_2EAPPEND_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EBIT1_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT1_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT1_2E0,X0_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EBIT2_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EBIT2_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2EBIT2_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Esptree_2EBN_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27a),X1_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2EBN_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),c_2Esptree_2EBN_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esptree_2EBN_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27b),X1_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2EBN_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27b),app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27b)),c_2Esptree_2EBN_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Esptree_2EBS_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27a),X1_2E0: A_27a,X2_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2EBS_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),c_2Esptree_2EBS_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Esptree_2EBS_2E3_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27b),X1_2E0: A_27b,X2_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2EBS_2E3(A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27b)),app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27b))),c_2Esptree_2EBS_2E0(A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2ECARD_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ECARD_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Enum_2Enum,c_2Epred__set_2ECARD_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool,X2_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool)),c_2Ebool_2ECOND_2E0(tyop_2Emin_2Ebool),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Enum_2Enum] : ( c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Ebool_2ECOND_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eoption_2Eoption(A_27a),X2_2E0: tyop_2Eoption_2Eoption(A_27a)] : ( c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a))),c_2Ebool_2ECOND_2E0(tyop_2Eoption_2Eoption(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eoption_2Eoption(A_27b),X2_2E0: tyop_2Eoption_2Eoption(A_27b)] : ( c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27b),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27b))),c_2Ebool_2ECOND_2E0(tyop_2Eoption_2Eoption(A_27b)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Eoption_2Eoption_28tyop_2Eone_2Eone_29,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),X2_2E0: tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)] : ( c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),app_2E2(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone))),c_2Ebool_2ECOND_2E0(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Ebool_2ECOND_2E3_2Emono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Esptree_2Espt(A_27a),X2_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Ebool_2ECOND_2E3(tyop_2Esptree_2Espt(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),c_2Ebool_2ECOND_2E0(tyop_2Esptree_2Espt(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ECONS_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Elist_2ECONS_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: A_27b,X1_2E0: tyop_2Elist_2Elist(A_27b)] : ( c_2Elist_2ECONS_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),c_2Elist_2ECONS_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2ECONS_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),c_2Elist_2ECONS_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2ECONS_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))] : ( c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),c_2Elist_2ECONS_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Eind__type_2ECONSTR_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: A_27a,X2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a))] : ( c_2Eind__type_2ECONSTR_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Eind__type_2Erecspace(A_27a))),c_2Eind__type_2ECONSTR_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2EDATATYPE_2E1_2Emono_2Etyop_2Emin_2Ebool,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] : ( c_2Ebool_2EDATATYPE_2E1(tyop_2Emin_2Ebool,X0_2E0) = app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2EDATATYPE_2E0(tyop_2Emin_2Ebool),X0_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EDELETE_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Enum_2Enum] : ( c_2Epred__set_2EDELETE_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epred__set_2EDELETE_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EDIFF_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDIFF_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epred__set_2EDIFF_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EDISJOINT_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EDISJOINT_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2EDISJOINT_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Earithmetic_2EDIV_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EDIV_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Earithmetic_2EDIV_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EEL_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EEL_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),A_27a),c_2Elist_2EEL_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2EEVEN_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2EEVEN_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Eind__type_2EFCONS_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eind__type_2Erecspace(A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a))] : ( c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a))),c_2Eind__type_2EFCONS_2E0(tyop_2Eind__type_2Erecspace(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epred__set_2EFINITE_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,c_2Epred__set_2EFINITE_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDL_2E3_2Emono_2EA_27a_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Esptree_2Espt_28A_27a_29_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))),X1_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),X2_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EFOLDL_2E3(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))),c_2Elist_2EFOLDL_2E0(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),X1_2E0: tyop_2Esptree_2Espt(A_27a),X2_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2EFOLDR_2E3(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Esptree_2Espt(A_27a))),c_2Elist_2EFOLDR_2E0(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2EFOLDR_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(A_27b,A_27b)),X1_2E0: A_27b,X2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))] : ( c_2Elist_2EFOLDR_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(A_27b,A_27b)),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),A_27b)),c_2Elist_2EFOLDR_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EFST_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b)] : ( c_2Epair_2EFST_2E1(tyop_2Enum_2Enum,A_27b,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),tyop_2Enum_2Enum,c_2Epair_2EFST_2E0(tyop_2Enum_2Enum,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Ecombin_2EI_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Ecombin_2EI_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27a)] : ( c_2Ecombin_2EI_2E1(tyop_2Eoption_2Eoption(A_27a),X0_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a),c_2Ecombin_2EI_2E0(tyop_2Eoption_2Eoption(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2EI_2E1_2Emono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Ecombin_2EI_2E1(tyop_2Esptree_2Espt(A_27a),X0_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a),c_2Ecombin_2EI_2E0(tyop_2Esptree_2Espt(A_27a)),X0_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EIMAGE_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epred__set_2EIMAGE_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a,X1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2EIN_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool)] : ( c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Ebool_2EIN_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EINSERT_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINSERT_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epred__set_2EINSERT_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EINTER_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EINTER_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epred__set_2EINTER_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: A_27b] : ( c_2Ecombin_2EK_2E1(A_27b,A_27a,X0_2E0) = app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,A_27b),c_2Ecombin_2EK_2E0(A_27b,A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ecombin_2EK_2E1_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: A_27b] : ( c_2Ecombin_2EK_2E1(A_27b,A_27c,X0_2E0) = app_2E2(A_27b,tyop_2Emin_2Efun(A_27c,A_27b),c_2Ecombin_2EK_2E0(A_27b,A_27c),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELENGTH_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELENGTH_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Enum_2Enum,c_2Elist_2ELENGTH_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),X1_2E0: tyop_2Enum_2Enum] : ( c_2Ebool_2ELET_2E2(tyop_2Enum_2Enum,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,A_27a,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),c_2Ebool_2ELET_2E0(tyop_2Enum_2Enum,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ELET_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),X1_2E0: tyop_2Enum_2Enum] : ( c_2Ebool_2ELET_2E2(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),c_2Ebool_2ELET_2E0(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2ELIST__TO__SET_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Elist_2ELIST__TO__SET_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq1_2Ec_2Elist_2ELIST__TO__SET_2E1_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))] : ( c_2Elist_2ELIST__TO__SET_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Ebool),c_2Elist_2ELIST__TO__SET_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Esptree_2ELS_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a] : ( c_2Esptree_2ELS_2E1(A_27a,X0_2E0) = app_2E2(A_27a,tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELS_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Esptree_2ELS_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: A_27b] : ( c_2Esptree_2ELS_2E1(A_27b,X0_2E0) = app_2E2(A_27b,tyop_2Esptree_2Espt(A_27b),c_2Esptree_2ELS_2E0(A_27b),X0_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Elist_2EMAP_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27a),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EMAP_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27b),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(A_27b)),c_2Elist_2EMAP_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2Etyop_2Enum_2Enum,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Enum_2Enum),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Enum_2Enum)),c_2Elist_2EMAP_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Elist_2EMAP_2E2_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27b_29_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b))] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),c_2Elist_2EMAP_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Earithmetic_2ENUMERAL_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Earithmetic_2ENUMERAL_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Earithmetic_2ENUMERAL_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Eoption_2Eoption(A_27a)] : ( c_2Eoption_2EOPTION__MAP_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),c_2Eoption_2EOPTION__MAP_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Eoption_2EOPTION__MAP_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0: tyop_2Eoption_2Eoption(A_27b)] : ( c_2Eoption_2EOPTION__MAP_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a)),c_2Eoption_2EOPTION__MAP_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b)] : ( c_2Epair_2ESND_2E1(tyop_2Enum_2Enum,A_27b,X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),A_27b,c_2Epair_2ESND_2E0(tyop_2Enum_2Enum,A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2ESND_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))] : ( c_2Epair_2ESND_2E1(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a),X0_2E0) = app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),tyop_2Esptree_2Espt(A_27a),c_2Epair_2ESND_2E0(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: A_27a] : ( c_2Eoption_2ESOME_2E1(A_27a,X0_2E0) = app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: A_27b] : ( c_2Eoption_2ESOME_2E1(A_27b,X0_2E0) = app_2E2(A_27b,tyop_2Eoption_2Eoption(A_27b),c_2Eoption_2ESOME_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Eoption_2ESOME_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
! [X0_2E0: tyop_2Eone_2Eone] : ( c_2Eoption_2ESOME_2E1(tyop_2Eone_2Eone,X0_2E0) = app_2E2(tyop_2Eone_2Eone,tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Eoption_2ESOME_2E0(tyop_2Eone_2Eone),X0_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2ESUBSET_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2ESUBSET_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Ebool),c_2Epred__set_2ESUBSET_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Enum_2ESUC_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Enum_2ESUC_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Enum_2ESUC_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2ETYPE__DEFINITION_2E2_2Emono_2Etyop_2Eind__type_2Erecspace_28A_27a_29_20mono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eind__type_2Erecspace(A_27a))] : ( c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Esptree_2Espt(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eind__type_2Erecspace(A_27a)),tyop_2Emin_2Ebool),c_2Ebool_2ETYPE__DEFINITION_2E0(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Esptree_2Espt(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27a_20mono_2Etyop_2Emin_2Efun_28A_27b_2CA_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b)))] : ( c_2Epair_2EUNCURRY_2E1(tyop_2Enum_2Enum,A_27a,tyop_2Emin_2Efun(A_27b,A_27b),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(A_27b,A_27b)),c_2Epair_2EUNCURRY_2E0(tyop_2Enum_2Enum,A_27a,tyop_2Emin_2Efun(A_27b,A_27b)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2EA_27b_20mono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))] : ( c_2Epair_2EUNCURRY_2E1(tyop_2Enum_2Enum,A_27b,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Epair_2EUNCURRY_2E0(tyop_2Enum_2Enum,A_27b,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X0_2E0) ) ).
tff(arityeq1_2Ec_2Epair_2EUNCURRY_2E1_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Esptree_2Espt_28A_27a_29_20mono_2Etyop_2Emin_2Efun_28A_27a_2Ctyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2Ctyop_2Esptree_2Espt_28A_27a_29_29_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))))] : ( c_2Epair_2EUNCURRY_2E1(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))))),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))),c_2Epair_2EUNCURRY_2E0(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))),X0_2E0) ) ).
tff(arityeq2_2Ec_2Epred__set_2EUNION_2E2_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( c_2Epred__set_2EUNION_2E2(tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),c_2Epred__set_2EUNION_2E0(tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWF_2E1(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E0(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWF_2E1(tyop_2Enum_2Enum,X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E0(tyop_2Enum_2Enum),X0_2E0) ) ).
tff(arityeq1_2Ec_2Erelation_2EWF_2E1_2Emono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool))] : ( c_2Erelation_2EWF_2E1(tyop_2Esptree_2Espt(A_27a),X0_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,c_2Erelation_2EWF_2E0(tyop_2Esptree_2Espt(A_27a)),X0_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_29_20mono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)))] : ( c_2Erelation_2EWFREC_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a))),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a))),c_2Erelation_2EWFREC_2E0(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Enum_2Enum_20mono_2Etyop_2Enum_2Enum,axiom,
! [X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum))] : ( c_2Erelation_2EWFREC_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),c_2Erelation_2EWFREC_2E0(tyop_2Enum_2Enum,tyop_2Enum_2Enum),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Erelation_2EWFREC_2E2_2Emono_2Etyop_2Esptree_2Espt_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),X1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)))] : ( c_2Erelation_2EWFREC_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a))),c_2Erelation_2EWFREC_2E0(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Ebool_2E_5C_2F_2E2,axiom,
! [X0_2E0: tyop_2Emin_2Ebool,X1_2E0: tyop_2Emin_2Ebool] :
( ( p(X0_2E0)
| p(X1_2E0) )
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Efun(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool),c_2Ebool_2E_5C_2F_2E0,X0_2E0),X1_2E0)) ) ).
tff(arityeq1_2Ec_2Epred__set_2Ecount_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Epred__set_2Ecount_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Epred__set_2Ecount_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Esptree_2Edelete_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Edelete_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),c_2Esptree_2Edelete_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esptree_2Edifference_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27a),X1_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Edifference_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),c_2Esptree_2Edifference_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esptree_2Edifference_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27a),X1_2E0: tyop_2Esptree_2Espt(A_27c)] : ( c_2Esptree_2Edifference_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27c),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27c),tyop_2Esptree_2Espt(A_27a)),c_2Esptree_2Edifference_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Esptree_2Edomain_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Edomain_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Esptree_2Edomain_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Edomain_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Esptree_2Edomain_2E1_2Emono_2EA_27c,axiom,
! [A_27c: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27c)] : ( c_2Esptree_2Edomain_2E1(A_27c,X0_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27c),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E0(A_27c),X0_2E0) ) ).
tff(arityeq1_2Ec_2Esptree_2Edomain_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
! [X0_2E0: tyop_2Esptree_2Espt(tyop_2Eone_2Eone)] : ( c_2Esptree_2Edomain_2E1(tyop_2Eone_2Eone,X0_2E0) = app_2E2(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),c_2Esptree_2Edomain_2E0(tyop_2Eone_2Eone),X0_2E0) ) ).
tff(arityeq2_2Ec_2Esptree_2Efilter__v_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),X1_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Efilter__v_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),c_2Esptree_2Efilter__v_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq4_2Ec_2Esptree_2Efoldi_2E4_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),X1_2E0: tyop_2Enum_2Enum,X2_2E0: A_27b,X3_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Efoldi_2E4(A_27b,A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b))),c_2Esptree_2Efoldi_2E0(A_27b,A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq4_2Ec_2Esptree_2Efoldi_2E4_2Emono_2Etyop_2Emin_2Efun_28tyop_2Enum_2Enum_2Ctyop_2Emin_2Ebool_29_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),X3_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Efoldi_2E4(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)))),c_2Esptree_2Efoldi_2E0(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq4_2Ec_2Esptree_2Efoldi_2E4_2Emono_2Etyop_2Elist_2Elist_28A_27b_29_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)))),X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Elist_2Elist(A_27b),X3_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Efoldi_2E4(tyop_2Elist_2Elist(A_27b),A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(A_27b),app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(A_27b)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(A_27b))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(A_27b)))),c_2Esptree_2Efoldi_2E0(tyop_2Elist_2Elist(A_27b),A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq3_2Ec_2Esptree_2Efoldi_2E3_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_29_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))] : ( c_2Esptree_2Efoldi_2E3(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),c_2Esptree_2Efoldi_2E0(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq4_2Ec_2Esptree_2Efoldi_2E4_2Emono_2Etyop_2Elist_2Elist_28tyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_29_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X3_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Efoldi_2E4(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),A_27a,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),c_2Esptree_2Efoldi_2E0(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),A_27a),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq4_2Ec_2Esptree_2Efoldi_2E4_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),X1_2E0: tyop_2Enum_2Enum,X2_2E0: A_27a,X3_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Efoldi_2E4(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27b),A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),A_27a))),c_2Esptree_2Efoldi_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0) ) ).
tff(arityeq1_2Ec_2Esptree_2EfromAList_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))] : ( c_2Esptree_2EfromAList_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EfromAList_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Esptree_2EfromAList_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b))] : ( c_2Esptree_2EfromAList_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b)),tyop_2Esptree_2Espt(A_27b),c_2Esptree_2EfromAList_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Esptree_2EfromList_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Esptree_2EfromList_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Esptree_2Espt(A_27a),c_2Esptree_2EfromList_2E0(A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Esptree_2Einsert_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: A_27a,X2_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Einsert_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),c_2Esptree_2Einsert_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Esptree_2Einsert_2E3_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: A_27b,X2_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Einsert_2E3(A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27b),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27b)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27b))),c_2Esptree_2Einsert_2E0(A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Esptree_2Einsert_2E3_2Emono_2Etyop_2Eone_2Eone,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Eone_2Eone,X2_2E0: tyop_2Esptree_2Espt(tyop_2Eone_2Eone)] : ( c_2Esptree_2Einsert_2E3(tyop_2Eone_2Eone,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone),app_2E2(tyop_2Eone_2Eone,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Eone_2Eone,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone))),c_2Esptree_2Einsert_2E0(tyop_2Eone_2Eone),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Esptree_2Einter_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27a),X1_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Einter_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),c_2Esptree_2Einter_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esptree_2Einter_2E2_2Emono_2EA_27a_20mono_2EA_27c,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27a),X1_2E0: tyop_2Esptree_2Espt(A_27c)] : ( c_2Esptree_2Einter_2E2(A_27a,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27c),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27c),tyop_2Esptree_2Espt(A_27a)),c_2Esptree_2Einter_2E0(A_27a,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esptree_2Einter_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27b),X1_2E0: tyop_2Esptree_2Espt(A_27c)] : ( c_2Esptree_2Einter_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27c),tyop_2Esptree_2Espt(A_27b),app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27c),tyop_2Esptree_2Espt(A_27b)),c_2Esptree_2Einter_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esptree_2Einter_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27c),X1_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Einter_2E2(A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27c),app_2E2(tyop_2Esptree_2Espt(A_27c),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27c)),c_2Esptree_2Einter_2E0(A_27c,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esptree_2Einter__eq_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27a),X1_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Einter__eq_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),c_2Esptree_2Einter__eq_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Elist_2Elist__CASE_2E3_2Emono_2Etyop_2Epair_2Eprod_28tyop_2Enum_2Enum_2CA_27a_29_20mono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),X1_2E0: tyop_2Esptree_2Espt(A_27a),X2_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)))] : ( c_2Elist_2Elist__CASE_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Esptree_2Espt(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a))),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a))),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a))),tyop_2Esptree_2Espt(A_27a))),c_2Elist_2Elist__CASE_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Esptree_2Espt(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Esptree_2Elist__insert_2E2,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum),X1_2E0: tyop_2Esptree_2Espt(tyop_2Eone_2Eone)] : ( c_2Esptree_2Elist__insert_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone),app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone)),c_2Esptree_2Elist__insert_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Esptree_2Elist__to__num__set_2E1,axiom,
! [X0_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Esptree_2Elist__to__num__set_2E1(X0_2E0) = app_2E2(tyop_2Elist_2Elist(tyop_2Enum_2Enum),tyop_2Esptree_2Espt(tyop_2Eone_2Eone),c_2Esptree_2Elist__to__num__set_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Esptree_2Elookup_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Elookup_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)),c_2Esptree_2Elookup_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esptree_2Elookup_2E2_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Elookup_2E2(A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Eoption_2Eoption(A_27b)),c_2Esptree_2Elookup_2E0(A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esptree_2Elookup_2E2_2Emono_2Etyop_2Eone_2Eone,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Esptree_2Espt(tyop_2Eone_2Eone)] : ( c_2Esptree_2Elookup_2E2(tyop_2Eone_2Eone,X0_2E0,X1_2E0) = app_2E2(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Eoption_2Eoption(tyop_2Eone_2Eone)),c_2Esptree_2Elookup_2E0(tyop_2Eone_2Eone),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Esptree_2Elrnext_2E1,axiom,
! [X0_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Elrnext_2E1(X0_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Esptree_2Elrnext_2E0,X0_2E0) ) ).
tff(arityeq2_2Ec_2Esptree_2Emap_2E2_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X1_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Emap_2E2(A_27b,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27b)),c_2Esptree_2Emap_2E0(A_27b,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esptree_2Emap_2E2_2Emono_2EA_27c_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,A_27c),X1_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Emap_2E2(A_27c,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27c),app_2E2(tyop_2Emin_2Efun(A_27a,A_27c),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27c)),c_2Esptree_2Emap_2E0(A_27c,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esptree_2Emap_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27a),X1_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Emap_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),c_2Esptree_2Emap_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esptree_2Emap_2E2_2Emono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Emap_2E2(A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27c),app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27c)),c_2Esptree_2Emap_2E0(A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esptree_2Emap_2E2_2Emono_2EA_27b_20mono_2EA_27c,axiom,
! [A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27c,A_27b),X1_2E0: tyop_2Esptree_2Espt(A_27c)] : ( c_2Esptree_2Emap_2E2(A_27b,A_27c,X0_2E0,X1_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27c),tyop_2Esptree_2Espt(A_27b),app_2E2(tyop_2Emin_2Efun(A_27c,A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27c),tyop_2Esptree_2Espt(A_27b)),c_2Esptree_2Emap_2E0(A_27b,A_27c),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esptree_2Emapi_2E2_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),X1_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Emapi_2E2(A_27a,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),c_2Esptree_2Emapi_2E0(A_27a,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Esptree_2Emapi0_2E3_2Emono_2EA_27b_20mono_2EA_27a,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Emapi0_2E3(A_27b,A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27b),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27b)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27b))),c_2Esptree_2Emapi0_2E0(A_27b,A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Esptree_2Emapi0_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),X1_2E0: tyop_2Enum_2Enum,X2_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Emapi0_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),c_2Esptree_2Emapi0_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Esptree_2Emk__BN_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27a),X1_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Emk__BN_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),c_2Esptree_2Emk__BN_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Esptree_2Emk__BS_2E3_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27a),X1_2E0: A_27a,X2_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Emk__BS_2E3(A_27a,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),c_2Esptree_2Emk__BS_2E0(A_27a),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Esptree_2Emk__wf_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Emk__wf_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Emk__wf_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Esptree_2Emk__wf_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Emk__wf_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27b),c_2Esptree_2Emk__wf_2E0(A_27b),X0_2E0) ) ).
tff(arityeq2_2Ec_2Ecombin_2Eo_2E2_2Emono_2EA_27a_20mono_2EA_27c_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,A_27c),X1_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Ecombin_2Eo_2E2(A_27a,A_27c,A_27b,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c),app_2E2(tyop_2Emin_2Efun(A_27b,A_27c),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(A_27a,A_27c)),c_2Ecombin_2Eo_2E0(A_27a,A_27c,A_27b),X0_2E0),X1_2E0) ) ).
tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27a),X1_2E0: tyop_2Eoption_2Eoption(A_27a),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))] : ( c_2Eoption_2Eoption__CASE_2E3(A_27a,tyop_2Eoption_2Eoption(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2Eoption__CASE_2E0(A_27a,tyop_2Eoption_2Eoption(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27a),X1_2E0: tyop_2Eoption_2Eoption(A_27b),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))] : ( c_2Eoption_2Eoption__CASE_2E3(A_27a,tyop_2Eoption_2Eoption(A_27b),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Eoption_2Eoption(A_27b)),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),tyop_2Eoption_2Eoption(A_27b))),c_2Eoption_2Eoption__CASE_2E0(A_27a,tyop_2Eoption_2Eoption(A_27b)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq3_2Ec_2Eoption_2Eoption__CASE_2E3_2Emono_2EA_27b_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Eoption_2Eoption(A_27b),X1_2E0: tyop_2Eoption_2Eoption(A_27a),X2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))] : ( c_2Eoption_2Eoption__CASE_2E3(A_27b,tyop_2Eoption_2Eoption(A_27a),X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),tyop_2Eoption_2Eoption(A_27a))),c_2Eoption_2Eoption__CASE_2E0(A_27b,tyop_2Eoption_2Eoption(A_27a)),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Esptree_2Espt_28A_27a_29_20mono_2Etyop_2Enum_2Enum_20mono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),X1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Enum_2Enum,A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))),tyop_2Esptree_2Espt(A_27a)),c_2Epair_2Epair__CASE_2E0(tyop_2Esptree_2Espt(A_27a),tyop_2Enum_2Enum,A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Epair_2Epair__CASE_2E2_2Emono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29_20mono_2Etyop_2Eoption_2Eoption_28A_27b_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),X1_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a)))] : ( c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b),X0_2E0,X1_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a))),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Epair_2Eprod(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a))),tyop_2Eoption_2Eoption(A_27a)),c_2Epair_2Epair__CASE_2E0(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b)),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Esptree_2Esize_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Esize_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Enum_2Enum,c_2Esptree_2Esize_2E0(A_27a),X0_2E0) ) ).
tff(arityeq5_2Ec_2Esptree_2Espt__CASE_2E5_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27a),X1_2E0: A_27b,X2_2E0: tyop_2Emin_2Efun(A_27a,A_27b),X3_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),X4_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)))] : ( c_2Esptree_2Espt__CASE_2E5(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0,X3_2E0,X4_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b))),A_27b,app_2E2(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b))),A_27b),app_2E2(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b))),A_27b)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b))),A_27b))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,A_27b),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b))),A_27b)))),c_2Esptree_2Espt__CASE_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0),X3_2E0),X4_2E0) ) ).
tff(arityeq5_2Ec_2Esptree_2Espt__CASE_2E5_2Emono_2EA_27a_20mono_2Etyop_2Eoption_2Eoption_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27a),X1_2E0: tyop_2Eoption_2Eoption(A_27a),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),X3_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a))),X4_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a))))] : ( c_2Esptree_2Espt__CASE_2E5(A_27a,tyop_2Eoption_2Eoption(A_27a),X0_2E0,X1_2E0,X2_2E0,X3_2E0,X4_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)))),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)))),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)))),tyop_2Eoption_2Eoption(A_27a))),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)))),tyop_2Eoption_2Eoption(A_27a)))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)))),tyop_2Eoption_2Eoption(A_27a))))),c_2Esptree_2Espt__CASE_2E0(A_27a,tyop_2Eoption_2Eoption(A_27a)),X0_2E0),X1_2E0),X2_2E0),X3_2E0),X4_2E0) ) ).
tff(arityeq5_2Ec_2Esptree_2Espt__CASE_2E5_2Emono_2EA_27a_20mono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27a),X1_2E0: tyop_2Esptree_2Espt(A_27a),X2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),X3_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),X4_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))] : ( c_2Esptree_2Espt__CASE_2E5(A_27a,tyop_2Esptree_2Espt(A_27a),X0_2E0,X1_2E0,X2_2E0,X3_2E0,X4_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),tyop_2Esptree_2Espt(A_27a)))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),tyop_2Esptree_2Espt(A_27a))))),c_2Esptree_2Espt__CASE_2E0(A_27a,tyop_2Esptree_2Espt(A_27a)),X0_2E0),X1_2E0),X2_2E0),X3_2E0),X4_2E0) ) ).
tff(arityeq5_2Ec_2Esptree_2Espt__CASE_2E5_2Emono_2EA_27b_20mono_2Etyop_2Esptree_2Espt_28A_27a_29,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27b),X1_2E0: tyop_2Esptree_2Espt(A_27a),X2_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),X3_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),X4_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))] : ( c_2Esptree_2Espt__CASE_2E5(A_27b,tyop_2Esptree_2Espt(A_27a),X0_2E0,X1_2E0,X2_2E0,X3_2E0,X4_2E0) = app_2E2(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),tyop_2Esptree_2Espt(A_27a)))),app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),tyop_2Esptree_2Espt(A_27a))))),c_2Esptree_2Espt__CASE_2E0(A_27b,tyop_2Esptree_2Espt(A_27a)),X0_2E0),X1_2E0),X2_2E0),X3_2E0),X4_2E0) ) ).
tff(arityeq2_2Ec_2Esptree_2Espt__acc_2E2,axiom,
! [X0_2E0: tyop_2Enum_2Enum,X1_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Espt__acc_2E2(X0_2E0,X1_2E0) = app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),c_2Esptree_2Espt__acc_2E0,X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Esptree_2Espt__center_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Espt__center_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Espt__center_2E0(A_27a),X0_2E0) ) ).
tff(arityeq3_2Ec_2Esptree_2Espt__fold_2E3_2Emono_2EA_27a_20mono_2EA_27b,axiom,
! [A_27a: $tType,A_27b: $tType,X0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),X1_2E0: A_27a,X2_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Espt__fold_2E3(A_27a,A_27b,X0_2E0,X1_2E0,X2_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27b),A_27a,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),A_27a)),c_2Esptree_2Espt__fold_2E0(A_27a,A_27b),X0_2E0),X1_2E0),X2_2E0) ) ).
tff(arityeq1_2Ec_2Esptree_2Espt__left_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Espt__left_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Espt__left_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Esptree_2Espt__right_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Espt__right_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Espt__right_2E0(A_27a),X0_2E0) ) ).
tff(arityeq2_2Ec_2Esptree_2Espt__size_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),X1_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Espt__size_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Enum_2Enum),c_2Esptree_2Espt__size_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esptree_2Esubspt_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27a),X1_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Esubspt_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),c_2Esptree_2Esubspt_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esptree_2Esubspt_2E2_2Emono_2Etyop_2Eone_2Eone,axiom,
! [X0_2E0: tyop_2Esptree_2Espt(tyop_2Eone_2Eone),X1_2E0: tyop_2Esptree_2Espt(tyop_2Eone_2Eone)] : ( c_2Esptree_2Esubspt_2E2(tyop_2Eone_2Eone,X0_2E0,X1_2E0) = app_2E2(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Ebool,app_2E2(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Ebool),c_2Esptree_2Esubspt_2E0(tyop_2Eone_2Eone),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Esptree_2EtoAList_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2EtoAList_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),c_2Esptree_2EtoAList_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Esptree_2EtoAList_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2EtoAList_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b)),c_2Esptree_2EtoAList_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Esptree_2EtoList_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2EtoList_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(A_27a),c_2Esptree_2EtoList_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Esptree_2EtoList_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2EtoList_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Elist_2Elist(A_27b),c_2Esptree_2EtoList_2E0(A_27b),X0_2E0) ) ).
tff(arityeq2_2Ec_2Esptree_2EtoListA_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Elist_2Elist(A_27a),X1_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2EtoListA_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(A_27a),app_2E2(tyop_2Elist_2Elist(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Elist_2Elist(A_27a)),c_2Esptree_2EtoListA_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esptree_2Eunion_2E2_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27a),X1_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Eunion_2E2(A_27a,X0_2E0,X1_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),c_2Esptree_2Eunion_2E0(A_27a),X0_2E0),X1_2E0) ) ).
tff(arityeq2_2Ec_2Esptree_2Eunion_2E2_2Emono_2Etyop_2Eone_2Eone,axiom,
! [X0_2E0: tyop_2Esptree_2Espt(tyop_2Eone_2Eone),X1_2E0: tyop_2Esptree_2Espt(tyop_2Eone_2Eone)] : ( c_2Esptree_2Eunion_2E2(tyop_2Eone_2Eone,X0_2E0,X1_2E0) = app_2E2(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone),app_2E2(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Esptree_2Espt(tyop_2Eone_2Eone)),c_2Esptree_2Eunion_2E0(tyop_2Eone_2Eone),X0_2E0),X1_2E0) ) ).
tff(arityeq1_2Ec_2Esptree_2Ewf_2E1_2Emono_2EA_27a,axiom,
! [A_27a: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Ewf_2E1(A_27a,X0_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E0(A_27a),X0_2E0) ) ).
tff(arityeq1_2Ec_2Esptree_2Ewf_2E1_2Emono_2EA_27b,axiom,
! [A_27b: $tType,X0_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Ewf_2E1(A_27b,X0_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E0(A_27b),X0_2E0) ) ).
tff(arityeq1_2Ec_2Esptree_2Ewf_2E1_2Emono_2Etyop_2Eone_2Eone,axiom,
! [X0_2E0: tyop_2Esptree_2Espt(tyop_2Eone_2Eone)] : ( c_2Esptree_2Ewf_2E1(tyop_2Eone_2Eone,X0_2E0) = app_2E2(tyop_2Esptree_2Espt(tyop_2Eone_2Eone),tyop_2Emin_2Ebool,c_2Esptree_2Ewf_2E0(tyop_2Eone_2Eone),X0_2E0) ) ).
tff(arityeq1_2Ec_2Ebool_2E_7E_2E1,axiom,
! [X0_2E0: tyop_2Emin_2Ebool] :
( ~ p(X0_2E0)
<=> p(app_2E2(tyop_2Emin_2Ebool,tyop_2Emin_2Ebool,c_2Ebool_2E_7E_2E0,X0_2E0)) ) ).
tff(thm_2Esptree_2Efilter__v__def,axiom,
! [A_27a: $tType] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Esptree_2Efilter__v_2E2(A_27a,V0f_2E0,c_2Esptree_2ELN_2E0(A_27a)) = c_2Esptree_2ELN_2E0(A_27a) )
& ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V2x_2E0: A_27a] : ( c_2Esptree_2Efilter__v_2E2(A_27a,V1f_2E0,c_2Esptree_2ELS_2E1(A_27a,V2x_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Esptree_2Espt(A_27a),app_2E2(A_27a,tyop_2Emin_2Ebool,V1f_2E0,V2x_2E0),c_2Esptree_2ELS_2E1(A_27a,V2x_2E0),c_2Esptree_2ELN_2E0(A_27a)) )
& ! [V3f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V4l_2E0: tyop_2Esptree_2Espt(A_27a),V5r_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Efilter__v_2E2(A_27a,V3f_2E0,c_2Esptree_2EBN_2E2(A_27a,V4l_2E0,V5r_2E0)) = c_2Esptree_2Emk__BN_2E2(A_27a,c_2Esptree_2Efilter__v_2E2(A_27a,V3f_2E0,V4l_2E0),c_2Esptree_2Efilter__v_2E2(A_27a,V3f_2E0,V5r_2E0)) )
& ! [V6f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V7l_2E0: tyop_2Esptree_2Espt(A_27a),V8x_2E0: A_27a,V9r_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Efilter__v_2E2(A_27a,V6f_2E0,c_2Esptree_2EBS_2E3(A_27a,V7l_2E0,V8x_2E0,V9r_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Esptree_2Espt(A_27a),app_2E2(A_27a,tyop_2Emin_2Ebool,V6f_2E0,V8x_2E0),c_2Esptree_2Emk__BS_2E3(A_27a,c_2Esptree_2Efilter__v_2E2(A_27a,V6f_2E0,V7l_2E0),V8x_2E0,c_2Esptree_2Efilter__v_2E2(A_27a,V6f_2E0,V9r_2E0)),c_2Esptree_2Emk__BN_2E2(A_27a,c_2Esptree_2Efilter__v_2E2(A_27a,V6f_2E0,V7l_2E0),c_2Esptree_2Efilter__v_2E2(A_27a,V6f_2E0,V9r_2E0))) ) ) ).
tff(thm_2Esptree_2Espt__center__primitive__def,axiom,
! [A_27a: $tType,F3_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a))),F4_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)))),F2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] :
( ! [V4v7_2E0: tyop_2Esptree_2Espt(A_27a),V5v8_2E0: tyop_2Esptree_2Espt(A_27a)] : ( app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)),F3_2E0,V4v7_2E0),V5v8_2E0) = c_2Ecombin_2EI_2E1(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0(A_27a)) )
=> ( ! [V6t1_2E0: tyop_2Esptree_2Espt(A_27a),V7x_27_2E0: A_27a,V8t2_2E0: tyop_2Esptree_2Espt(A_27a)] : ( app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a))),F4_2E0,V6t1_2E0),V7x_27_2E0),V8t2_2E0) = c_2Ecombin_2EI_2E1(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(A_27a,V7x_27_2E0)) )
=> ( ! [V3x_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27a),F2_2E0,V3x_2E0) = c_2Ecombin_2EI_2E1(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ESOME_2E1(A_27a,V3x_2E0)) )
=> ( ! [V1spt__center_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)),V2a_2E0: tyop_2Esptree_2Espt(A_27a)] : ( app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a)),F1_2E0,V1spt__center_2E0),V2a_2E0) = c_2Esptree_2Espt__CASE_2E5(A_27a,tyop_2Eoption_2Eoption(A_27a),V2a_2E0,c_2Ecombin_2EI_2E1(tyop_2Eoption_2Eoption(A_27a),c_2Eoption_2ENONE_2E0(A_27a)),F2_2E0,F3_2E0,F4_2E0) )
=> ( ! [V0R_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool))] : ( app_2E2(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,F0_2E0,V0R_2E0) = c_2Erelation_2EWF_2E1(tyop_2Esptree_2Espt(A_27a),V0R_2E0) )
=> ( c_2Esptree_2Espt__center_2E0(A_27a) = c_2Erelation_2EWFREC_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Eoption_2Eoption(A_27a),c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),F0_2E0),F1_2E0) ) ) ) ) ) ) ).
tff(thm_2Esptree_2Espt__right__def,axiom,
! [A_27a: $tType] :
( ( c_2Esptree_2Espt__right_2E1(A_27a,c_2Esptree_2ELN_2E0(A_27a)) = c_2Esptree_2ELN_2E0(A_27a) )
& ! [V0x_2E0: A_27a] : ( c_2Esptree_2Espt__right_2E1(A_27a,c_2Esptree_2ELS_2E1(A_27a,V0x_2E0)) = c_2Esptree_2ELN_2E0(A_27a) )
& ! [V1t1_2E0: tyop_2Esptree_2Espt(A_27a),V2t2_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Espt__right_2E1(A_27a,c_2Esptree_2EBN_2E2(A_27a,V1t1_2E0,V2t2_2E0)) = V2t2_2E0 )
& ! [V3t1_2E0: tyop_2Esptree_2Espt(A_27a),V4x_2E0: A_27a,V5t2_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Espt__right_2E1(A_27a,c_2Esptree_2EBS_2E3(A_27a,V3t1_2E0,V4x_2E0,V5t2_2E0)) = V5t2_2E0 ) ) ).
tff(thm_2Esptree_2Espt__left__def,axiom,
! [A_27a: $tType] :
( ( c_2Esptree_2Espt__left_2E1(A_27a,c_2Esptree_2ELN_2E0(A_27a)) = c_2Esptree_2ELN_2E0(A_27a) )
& ! [V0x_2E0: A_27a] : ( c_2Esptree_2Espt__left_2E1(A_27a,c_2Esptree_2ELS_2E1(A_27a,V0x_2E0)) = c_2Esptree_2ELN_2E0(A_27a) )
& ! [V1t1_2E0: tyop_2Esptree_2Espt(A_27a),V2t2_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Espt__left_2E1(A_27a,c_2Esptree_2EBN_2E2(A_27a,V1t1_2E0,V2t2_2E0)) = V1t1_2E0 )
& ! [V3t1_2E0: tyop_2Esptree_2Espt(A_27a),V4x_2E0: A_27a,V5t2_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Espt__left_2E1(A_27a,c_2Esptree_2EBS_2E3(A_27a,V3t1_2E0,V4x_2E0,V5t2_2E0)) = V3t1_2E0 ) ) ).
tff(thm_2Esptree_2Emap__def,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : ( c_2Esptree_2Emap_2E2(A_27a,A_27b,V0f_2E0,c_2Esptree_2ELN_2E0(A_27b)) = c_2Esptree_2ELN_2E0(A_27a) )
& ! [V1f_2E0: tyop_2Emin_2Efun(A_27b,A_27a),V2a_2E0: A_27b] : ( c_2Esptree_2Emap_2E2(A_27a,A_27b,V1f_2E0,c_2Esptree_2ELS_2E1(A_27b,V2a_2E0)) = c_2Esptree_2ELS_2E1(A_27a,app_2E2(A_27b,A_27a,V1f_2E0,V2a_2E0)) )
& ! [V3f_2E0: tyop_2Emin_2Efun(A_27b,A_27a),V4t1_2E0: tyop_2Esptree_2Espt(A_27b),V5t2_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Emap_2E2(A_27a,A_27b,V3f_2E0,c_2Esptree_2EBN_2E2(A_27b,V4t1_2E0,V5t2_2E0)) = c_2Esptree_2EBN_2E2(A_27a,c_2Esptree_2Emap_2E2(A_27a,A_27b,V3f_2E0,V4t1_2E0),c_2Esptree_2Emap_2E2(A_27a,A_27b,V3f_2E0,V5t2_2E0)) )
& ! [V6f_2E0: tyop_2Emin_2Efun(A_27b,A_27a),V7t1_2E0: tyop_2Esptree_2Espt(A_27b),V8a_2E0: A_27b,V9t2_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Emap_2E2(A_27a,A_27b,V6f_2E0,c_2Esptree_2EBS_2E3(A_27b,V7t1_2E0,V8a_2E0,V9t2_2E0)) = c_2Esptree_2EBS_2E3(A_27a,c_2Esptree_2Emap_2E2(A_27a,A_27b,V6f_2E0,V7t1_2E0),app_2E2(A_27b,A_27a,V6f_2E0,V8a_2E0),c_2Esptree_2Emap_2E2(A_27a,A_27b,V6f_2E0,V9t2_2E0)) ) ) ).
tff(thm_2Esptree_2EfromAList__primitive__def,axiom,
! [A_27a: $tType,F3_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))))),F2_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] :
( ! [V4fromAList_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),V7xs_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V8x_2E0: tyop_2Enum_2Enum,V9y_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)))),F3_2E0,V4fromAList_2E0),V7xs_2E0),V8x_2E0),V9y_2E0) = c_2Ecombin_2EI_2E1(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Einsert_2E3(A_27a,V8x_2E0,V9y_2E0,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a),V4fromAList_2E0,V7xs_2E0))) )
=> ( ! [V4fromAList_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),V6v_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),V7xs_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a))),F2_2E0,V4fromAList_2E0),V6v_2E0),V7xs_2E0) = c_2Epair_2Epair__CASE_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Enum_2Enum,A_27a,V6v_2E0,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)))),F3_2E0,V4fromAList_2E0),V7xs_2E0)) )
=> ( ! [V4fromAList_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),V5a_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),F1_2E0,V4fromAList_2E0),V5a_2E0) = c_2Elist_2Elist__CASE_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Esptree_2Espt(A_27a),V5a_2E0,c_2Ecombin_2EI_2E1(tyop_2Esptree_2Espt(A_27a),c_2Esptree_2ELN_2E0(A_27a)),app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a))),F2_2E0,V4fromAList_2E0)) )
=> ( ! [V0R_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool))] :
( p(app_2E2(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,F0_2E0,V0R_2E0))
<=> ( p(c_2Erelation_2EWF_2E1(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V0R_2E0))
& ! [V1y_2E0: A_27a,V2x_2E0: tyop_2Enum_2Enum,V3xs_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool,app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool),V0R_2E0,V3xs_2E0),c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,A_27a,V2x_2E0,V1y_2E0),V3xs_2E0))) ) )
=> ( c_2Esptree_2EfromAList_2E0(A_27a) = c_2Erelation_2EWFREC_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Esptree_2Espt(A_27a),c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)),F0_2E0),F1_2E0) ) ) ) ) ) ).
tff(thm_2Esptree_2Emk__wf__def,axiom,
! [A_27a: $tType] :
( ( c_2Esptree_2Emk__wf_2E1(A_27a,c_2Esptree_2ELN_2E0(A_27a)) = c_2Esptree_2ELN_2E0(A_27a) )
& ! [V0x_2E0: A_27a] : ( c_2Esptree_2Emk__wf_2E1(A_27a,c_2Esptree_2ELS_2E1(A_27a,V0x_2E0)) = c_2Esptree_2ELS_2E1(A_27a,V0x_2E0) )
& ! [V1t1_2E0: tyop_2Esptree_2Espt(A_27a),V2t2_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Emk__wf_2E1(A_27a,c_2Esptree_2EBN_2E2(A_27a,V1t1_2E0,V2t2_2E0)) = c_2Esptree_2Emk__BN_2E2(A_27a,c_2Esptree_2Emk__wf_2E1(A_27a,V1t1_2E0),c_2Esptree_2Emk__wf_2E1(A_27a,V2t2_2E0)) )
& ! [V3t1_2E0: tyop_2Esptree_2Espt(A_27a),V4x_2E0: A_27a,V5t2_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Emk__wf_2E1(A_27a,c_2Esptree_2EBS_2E3(A_27a,V3t1_2E0,V4x_2E0,V5t2_2E0)) = c_2Esptree_2Emk__BS_2E3(A_27a,c_2Esptree_2Emk__wf_2E1(A_27a,V3t1_2E0),V4x_2E0,c_2Esptree_2Emk__wf_2E1(A_27a,V5t2_2E0)) ) ) ).
tff(thm_2Esptree_2EtoList__def,axiom,
! [A_27a: $tType,V0m_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2EtoList_2E1(A_27a,V0m_2E0) = c_2Esptree_2EtoListA_2E2(A_27a,c_2Elist_2ENIL_2E0(A_27a),V0m_2E0) ) ).
tff(thm_2Esptree_2EtoListA__def,axiom,
! [A_27a: $tType] :
( ! [V0acc_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Esptree_2EtoListA_2E2(A_27a,V0acc_2E0,c_2Esptree_2ELN_2E0(A_27a)) = V0acc_2E0 )
& ! [V1acc_2E0: tyop_2Elist_2Elist(A_27a),V2a_2E0: A_27a] : ( c_2Esptree_2EtoListA_2E2(A_27a,V1acc_2E0,c_2Esptree_2ELS_2E1(A_27a,V2a_2E0)) = c_2Elist_2ECONS_2E2(A_27a,V2a_2E0,V1acc_2E0) )
& ! [V3acc_2E0: tyop_2Elist_2Elist(A_27a),V4t1_2E0: tyop_2Esptree_2Espt(A_27a),V5t2_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2EtoListA_2E2(A_27a,V3acc_2E0,c_2Esptree_2EBN_2E2(A_27a,V4t1_2E0,V5t2_2E0)) = c_2Esptree_2EtoListA_2E2(A_27a,c_2Esptree_2EtoListA_2E2(A_27a,V3acc_2E0,V5t2_2E0),V4t1_2E0) )
& ! [V6acc_2E0: tyop_2Elist_2Elist(A_27a),V7t1_2E0: tyop_2Esptree_2Espt(A_27a),V8a_2E0: A_27a,V9t2_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2EtoListA_2E2(A_27a,V6acc_2E0,c_2Esptree_2EBS_2E3(A_27a,V7t1_2E0,V8a_2E0,V9t2_2E0)) = c_2Esptree_2EtoListA_2E2(A_27a,c_2Elist_2ECONS_2E2(A_27a,V8a_2E0,c_2Esptree_2EtoListA_2E2(A_27a,V6acc_2E0,V9t2_2E0)),V7t1_2E0) ) ) ).
tff(thm_2Esptree_2EtoAList__def,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))))] :
( ! [V0k_2E0: tyop_2Enum_2Enum,V1v_2E0: A_27a,V2a_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),F0_2E0,V0k_2E0),V1v_2E0),V2a_2E0) = c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,A_27a,V0k_2E0,V1v_2E0),V2a_2E0) )
=> ( c_2Esptree_2EtoAList_2E0(A_27a) = c_2Esptree_2Efoldi_2E3(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),A_27a,F0_2E0,c_2Enum_2E0_2E0,c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))) ) ) ).
tff(thm_2Esptree_2Emapi__def,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V1pt_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Emapi_2E2(A_27a,A_27b,V0f_2E0,V1pt_2E0) = c_2Esptree_2Emapi0_2E3(A_27a,A_27b,V0f_2E0,c_2Enum_2E0_2E0,V1pt_2E0) ) ).
tff(thm_2Esptree_2Emapi0__def,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))))))] :
( ! [V5f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V6i_2E0: tyop_2Enum_2Enum,V7t1_2E0: tyop_2Esptree_2Espt(A_27b),V8t2_2E0: tyop_2Esptree_2Espt(A_27b),V9inc_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))))),F0_2E0,V5f_2E0),V6i_2E0),V7t1_2E0),V8t2_2E0),V9inc_2E0) = c_2Esptree_2Emk__BN_2E2(A_27a,c_2Esptree_2Emapi0_2E3(A_27a,A_27b,V5f_2E0,c_2Earithmetic_2E_2B_2E2(V6i_2E0,c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V9inc_2E0)),V7t1_2E0),c_2Esptree_2Emapi0_2E3(A_27a,A_27b,V5f_2E0,c_2Earithmetic_2E_2B_2E2(V6i_2E0,V9inc_2E0),V8t2_2E0)) )
=> ( ! [V10f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V11i_2E0: tyop_2Enum_2Enum,V12t1_2E0: tyop_2Esptree_2Espt(A_27b),V13a_2E0: A_27b,V14t2_2E0: tyop_2Esptree_2Espt(A_27b),V15inc_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))))),F1_2E0,V10f_2E0),V11i_2E0),V12t1_2E0),V13a_2E0),V14t2_2E0),V15inc_2E0) = c_2Esptree_2Emk__BS_2E3(A_27a,c_2Esptree_2Emapi0_2E3(A_27a,A_27b,V10f_2E0,c_2Earithmetic_2E_2B_2E2(V11i_2E0,c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V15inc_2E0)),V12t1_2E0),app_2E2(A_27b,A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a),V10f_2E0,V11i_2E0),V13a_2E0),c_2Esptree_2Emapi0_2E3(A_27a,A_27b,V10f_2E0,c_2Earithmetic_2E_2B_2E2(V11i_2E0,V15inc_2E0),V14t2_2E0)) )
=> ( ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V1i_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Emapi0_2E3(A_27a,A_27b,V0f_2E0,V1i_2E0,c_2Esptree_2ELN_2E0(A_27b)) = c_2Esptree_2ELN_2E0(A_27a) )
& ! [V2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V3i_2E0: tyop_2Enum_2Enum,V4a_2E0: A_27b] : ( c_2Esptree_2Emapi0_2E3(A_27a,A_27b,V2f_2E0,V3i_2E0,c_2Esptree_2ELS_2E1(A_27b,V4a_2E0)) = c_2Esptree_2ELS_2E1(A_27a,app_2E2(A_27b,A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a),V2f_2E0,V3i_2E0),V4a_2E0)) )
& ! [V5f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V6i_2E0: tyop_2Enum_2Enum,V7t1_2E0: tyop_2Esptree_2Espt(A_27b),V8t2_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Emapi0_2E3(A_27a,A_27b,V5f_2E0,V6i_2E0,c_2Esptree_2EBN_2E2(A_27b,V7t1_2E0,V8t2_2E0)) = c_2Ebool_2ELET_2E2(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))))),F0_2E0,V5f_2E0),V6i_2E0),V7t1_2E0),V8t2_2E0),c_2Esptree_2Elrnext_2E1(V6i_2E0)) )
& ! [V10f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V11i_2E0: tyop_2Enum_2Enum,V12t1_2E0: tyop_2Esptree_2Espt(A_27b),V13a_2E0: A_27b,V14t2_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Emapi0_2E3(A_27a,A_27b,V10f_2E0,V11i_2E0,c_2Esptree_2EBS_2E3(A_27b,V12t1_2E0,V13a_2E0,V14t2_2E0)) = c_2Ebool_2ELET_2E2(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))))),F1_2E0,V10f_2E0),V11i_2E0),V12t1_2E0),V13a_2E0),V14t2_2E0),c_2Esptree_2Elrnext_2E1(V11i_2E0)) ) ) ) ) ).
tff(thm_2Esptree_2Efoldi__def,axiom,
! [A_27a: $tType,A_27b: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))))))),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))))))] :
( ! [V13f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),V14i_2E0: tyop_2Enum_2Enum,V17a_2E0: A_27b,V15acc_2E0: A_27a,V16t1_2E0: tyop_2Esptree_2Espt(A_27b),V18t2_2E0: tyop_2Esptree_2Espt(A_27b),V19inc_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27a,app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))))),F1_2E0,V13f_2E0),V14i_2E0),V17a_2E0),V15acc_2E0),V16t1_2E0),V18t2_2E0),V19inc_2E0) = c_2Esptree_2Efoldi_2E4(A_27a,A_27b,V13f_2E0,c_2Earithmetic_2E_2B_2E2(V14i_2E0,V19inc_2E0),app_2E2(A_27a,A_27a,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),V13f_2E0,V14i_2E0),V17a_2E0),c_2Esptree_2Efoldi_2E4(A_27a,A_27b,V13f_2E0,c_2Earithmetic_2E_2B_2E2(V14i_2E0,c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V19inc_2E0)),V15acc_2E0,V16t1_2E0)),V18t2_2E0) )
=> ( ! [V7f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),V8i_2E0: tyop_2Enum_2Enum,V9acc_2E0: A_27a,V10t1_2E0: tyop_2Esptree_2Espt(A_27b),V11t2_2E0: tyop_2Esptree_2Espt(A_27b),V12inc_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,A_27a,app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))))),F0_2E0,V7f_2E0),V8i_2E0),V9acc_2E0),V10t1_2E0),V11t2_2E0),V12inc_2E0) = c_2Esptree_2Efoldi_2E4(A_27a,A_27b,V7f_2E0,c_2Earithmetic_2E_2B_2E2(V8i_2E0,V12inc_2E0),c_2Esptree_2Efoldi_2E4(A_27a,A_27b,V7f_2E0,c_2Earithmetic_2E_2B_2E2(V8i_2E0,c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V12inc_2E0)),V9acc_2E0,V10t1_2E0),V11t2_2E0) )
=> ( ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),V1i_2E0: tyop_2Enum_2Enum,V2acc_2E0: A_27a] : ( c_2Esptree_2Efoldi_2E4(A_27a,A_27b,V0f_2E0,V1i_2E0,V2acc_2E0,c_2Esptree_2ELN_2E0(A_27b)) = V2acc_2E0 )
& ! [V3f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),V4i_2E0: tyop_2Enum_2Enum,V5acc_2E0: A_27a,V6a_2E0: A_27b] : ( c_2Esptree_2Efoldi_2E4(A_27a,A_27b,V3f_2E0,V4i_2E0,V5acc_2E0,c_2Esptree_2ELS_2E1(A_27b,V6a_2E0)) = app_2E2(A_27a,A_27a,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),V3f_2E0,V4i_2E0),V6a_2E0),V5acc_2E0) )
& ! [V7f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),V8i_2E0: tyop_2Enum_2Enum,V9acc_2E0: A_27a,V10t1_2E0: tyop_2Esptree_2Espt(A_27b),V11t2_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Efoldi_2E4(A_27a,A_27b,V7f_2E0,V8i_2E0,V9acc_2E0,c_2Esptree_2EBN_2E2(A_27b,V10t1_2E0,V11t2_2E0)) = c_2Ebool_2ELET_2E2(tyop_2Enum_2Enum,A_27a,app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))))),F0_2E0,V7f_2E0),V8i_2E0),V9acc_2E0),V10t1_2E0),V11t2_2E0),c_2Esptree_2Elrnext_2E1(V8i_2E0)) )
& ! [V13f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),V14i_2E0: tyop_2Enum_2Enum,V15acc_2E0: A_27a,V16t1_2E0: tyop_2Esptree_2Espt(A_27b),V17a_2E0: A_27b,V18t2_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Efoldi_2E4(A_27a,A_27b,V13f_2E0,V14i_2E0,V15acc_2E0,c_2Esptree_2EBS_2E3(A_27b,V16t1_2E0,V17a_2E0,V18t2_2E0)) = c_2Ebool_2ELET_2E2(tyop_2Enum_2Enum,A_27a,app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a),app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))),app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a))))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a))),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,A_27a)))))),F1_2E0,V13f_2E0),V14i_2E0),V17a_2E0),V15acc_2E0),V16t1_2E0),V18t2_2E0),c_2Esptree_2Elrnext_2E1(V14i_2E0)) ) ) ) ) ).
tff(thm_2Esptree_2Espt__TY__DEF,axiom,
! [A_27a: $tType,F4_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F3_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a)),F0_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool)] :
( ! [V13n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a),F4_2E0,V13n_2E0) = c_2Eind__type_2EBOTTOM_2E0(A_27a) )
=> ( ! [V9n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a),F3_2E0,V9n_2E0) = c_2Eind__type_2EBOTTOM_2E0(A_27a) )
=> ( ! [V6n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a),F2_2E0,V6n_2E0) = c_2Eind__type_2EBOTTOM_2E0(A_27a) )
=> ( ! [V4n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Eind__type_2Erecspace(A_27a),F1_2E0,V4n_2E0) = c_2Eind__type_2EBOTTOM_2E0(A_27a) )
=> ( ! [V1a0_27_2E0: tyop_2Eind__type_2Erecspace(A_27a)] :
( p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,F0_2E0,V1a0_27_2E0))
<=> ! [V2_27spt_27_2E0: tyop_2Emin_2Efun(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool)] :
( ! [V3a0_27_2E0: tyop_2Eind__type_2Erecspace(A_27a)] :
( ( ( V3a0_27_2E0 = c_2Eind__type_2ECONSTR_2E3(A_27a,c_2Enum_2E0_2E0,c_2Ebool_2EARB_2E0(A_27a),F1_2E0) )
| ? [V5a_2E0: A_27a] : ( V3a0_27_2E0 = c_2Eind__type_2ECONSTR_2E3(A_27a,c_2Enum_2ESUC_2E1(c_2Enum_2E0_2E0),V5a_2E0,F2_2E0) )
| ? [V7a0_2E0: tyop_2Eind__type_2Erecspace(A_27a),V8a1_2E0: tyop_2Eind__type_2Erecspace(A_27a)] :
( ( V3a0_27_2E0 = c_2Eind__type_2ECONSTR_2E3(A_27a,c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(c_2Enum_2E0_2E0)),c_2Ebool_2EARB_2E0(A_27a),c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(A_27a),V7a0_2E0,c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(A_27a),V8a1_2E0,F3_2E0))) )
& p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V2_27spt_27_2E0,V7a0_2E0))
& p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V2_27spt_27_2E0,V8a1_2E0)) )
| ? [V10a0_2E0: tyop_2Eind__type_2Erecspace(A_27a),V11a1_2E0: A_27a,V12a2_2E0: tyop_2Eind__type_2Erecspace(A_27a)] :
( ( V3a0_27_2E0 = c_2Eind__type_2ECONSTR_2E3(A_27a,c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(c_2Enum_2ESUC_2E1(c_2Enum_2E0_2E0))),V11a1_2E0,c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(A_27a),V10a0_2E0,c_2Eind__type_2EFCONS_2E2(tyop_2Eind__type_2Erecspace(A_27a),V12a2_2E0,F4_2E0))) )
& p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V2_27spt_27_2E0,V10a0_2E0))
& p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V2_27spt_27_2E0,V12a2_2E0)) ) )
=> p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V2_27spt_27_2E0,V3a0_27_2E0)) )
=> p(app_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Emin_2Ebool,V2_27spt_27_2E0,V1a0_27_2E0)) ) )
=> ? [V0rep_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Eind__type_2Erecspace(A_27a))] : p(c_2Ebool_2ETYPE__DEFINITION_2E2(tyop_2Eind__type_2Erecspace(A_27a),tyop_2Esptree_2Espt(A_27a),F0_2E0,V0rep_2E0)) ) ) ) ) ) ).
tff(thm_2Esptree_2Espt__case__def,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0v_2E0: A_27b,V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2f1_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),V3f2_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)))] : ( c_2Esptree_2Espt__CASE_2E5(A_27a,A_27b,c_2Esptree_2ELN_2E0(A_27a),V0v_2E0,V1f_2E0,V2f1_2E0,V3f2_2E0) = V0v_2E0 )
& ! [V4a_2E0: A_27a,V5v_2E0: A_27b,V6f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V7f1_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),V8f2_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)))] : ( c_2Esptree_2Espt__CASE_2E5(A_27a,A_27b,c_2Esptree_2ELS_2E1(A_27a,V4a_2E0),V5v_2E0,V6f_2E0,V7f1_2E0,V8f2_2E0) = app_2E2(A_27a,A_27b,V6f_2E0,V4a_2E0) )
& ! [V9a0_2E0: tyop_2Esptree_2Espt(A_27a),V10a1_2E0: tyop_2Esptree_2Espt(A_27a),V11v_2E0: A_27b,V12f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V13f1_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),V14f2_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)))] : ( c_2Esptree_2Espt__CASE_2E5(A_27a,A_27b,c_2Esptree_2EBN_2E2(A_27a,V9a0_2E0,V10a1_2E0),V11v_2E0,V12f_2E0,V13f1_2E0,V14f2_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),A_27b,app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b),V13f1_2E0,V9a0_2E0),V10a1_2E0) )
& ! [V15a0_2E0: tyop_2Esptree_2Espt(A_27a),V16a1_2E0: A_27a,V17a2_2E0: tyop_2Esptree_2Espt(A_27a),V18v_2E0: A_27b,V19f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V20f1_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),V21f2_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)))] : ( c_2Esptree_2Espt__CASE_2E5(A_27a,A_27b,c_2Esptree_2EBS_2E3(A_27a,V15a0_2E0,V16a1_2E0,V17a2_2E0),V18v_2E0,V19f_2E0,V20f1_2E0,V21f2_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),V21f2_2E0,V15a0_2E0),V16a1_2E0),V17a2_2E0) ) ) ).
tff(thm_2Esptree_2Espt__size__def,axiom,
! [A_27a: $tType] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum)] : ( c_2Esptree_2Espt__size_2E2(A_27a,V0f_2E0,c_2Esptree_2ELN_2E0(A_27a)) = c_2Enum_2E0_2E0 )
& ! [V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V2a_2E0: A_27a] : ( c_2Esptree_2Espt__size_2E2(A_27a,V1f_2E0,c_2Esptree_2ELS_2E1(A_27a,V2a_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),app_2E2(A_27a,tyop_2Enum_2Enum,V1f_2E0,V2a_2E0)) )
& ! [V3f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V4a0_2E0: tyop_2Esptree_2Espt(A_27a),V5a1_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Espt__size_2E2(A_27a,V3f_2E0,c_2Esptree_2EBN_2E2(A_27a,V4a0_2E0,V5a1_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2B_2E2(c_2Esptree_2Espt__size_2E2(A_27a,V3f_2E0,V4a0_2E0),c_2Esptree_2Espt__size_2E2(A_27a,V3f_2E0,V5a1_2E0))) )
& ! [V6f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Enum_2Enum),V7a0_2E0: tyop_2Esptree_2Espt(A_27a),V8a1_2E0: A_27a,V9a2_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Espt__size_2E2(A_27a,V6f_2E0,c_2Esptree_2EBS_2E3(A_27a,V7a0_2E0,V8a1_2E0,V9a2_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2B_2E2(c_2Esptree_2Espt__size_2E2(A_27a,V6f_2E0,V7a0_2E0),c_2Earithmetic_2E_2B_2E2(app_2E2(A_27a,tyop_2Enum_2Enum,V6f_2E0,V8a1_2E0),c_2Esptree_2Espt__size_2E2(A_27a,V6f_2E0,V9a2_2E0)))) ) ) ).
tff(thm_2Esptree_2Ewf__def,axiom,
! [A_27a: $tType] :
( ( c_2Esptree_2Ewf_2E1(A_27a,c_2Esptree_2ELN_2E0(A_27a)) = c_2Ebool_2ET_2E0 )
& ! [V0a_2E0: A_27a] : ( c_2Esptree_2Ewf_2E1(A_27a,c_2Esptree_2ELS_2E1(A_27a,V0a_2E0)) = c_2Ebool_2ET_2E0 )
& ! [V1t1_2E0: tyop_2Esptree_2Espt(A_27a),V2t2_2E0: tyop_2Esptree_2Espt(A_27a)] :
( p(c_2Esptree_2Ewf_2E1(A_27a,c_2Esptree_2EBN_2E2(A_27a,V1t1_2E0,V2t2_2E0)))
<=> ( p(c_2Esptree_2Ewf_2E1(A_27a,V1t1_2E0))
& p(c_2Esptree_2Ewf_2E1(A_27a,V2t2_2E0))
& ~ ( ( V1t1_2E0 = c_2Esptree_2ELN_2E0(A_27a) )
& ( V2t2_2E0 = c_2Esptree_2ELN_2E0(A_27a) ) ) ) )
& ! [V3t1_2E0: tyop_2Esptree_2Espt(A_27a),V4a_2E0: A_27a,V5t2_2E0: tyop_2Esptree_2Espt(A_27a)] :
( p(c_2Esptree_2Ewf_2E1(A_27a,c_2Esptree_2EBS_2E3(A_27a,V3t1_2E0,V4a_2E0,V5t2_2E0)))
<=> ( p(c_2Esptree_2Ewf_2E1(A_27a,V3t1_2E0))
& p(c_2Esptree_2Ewf_2E1(A_27a,V5t2_2E0))
& ~ ( ( V3t1_2E0 = c_2Esptree_2ELN_2E0(A_27a) )
& ( V5t2_2E0 = c_2Esptree_2ELN_2E0(A_27a) ) ) ) ) ) ).
tff(thm_2Esptree_2Edelete__def,axiom,
! [A_27a: $tType,F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( ! [V6k_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F2_2E0,V6k_2E0))
<=> ( V6k_2E0 = c_2Enum_2E0_2E0 ) )
=> ( ! [V3k_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F1_2E0,V3k_2E0))
<=> ( V3k_2E0 = c_2Enum_2E0_2E0 ) )
=> ( ! [V1k_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V1k_2E0))
<=> ( V1k_2E0 = c_2Enum_2E0_2E0 ) )
=> ( ! [V0k_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Edelete_2E2(A_27a,V0k_2E0,c_2Esptree_2ELN_2E0(A_27a)) = c_2Esptree_2ELN_2E0(A_27a) )
& ! [V1k_2E0: tyop_2Enum_2Enum,V2a_2E0: A_27a] : ( c_2Esptree_2Edelete_2E2(A_27a,V1k_2E0,c_2Esptree_2ELS_2E1(A_27a,V2a_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V1k_2E0),c_2Esptree_2ELN_2E0(A_27a),c_2Esptree_2ELS_2E1(A_27a,V2a_2E0)) )
& ! [V3k_2E0: tyop_2Enum_2Enum,V4t1_2E0: tyop_2Esptree_2Espt(A_27a),V5t2_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Edelete_2E2(A_27a,V3k_2E0,c_2Esptree_2EBN_2E2(A_27a,V4t1_2E0,V5t2_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F1_2E0,V3k_2E0),c_2Esptree_2EBN_2E2(A_27a,V4t1_2E0,V5t2_2E0),c_2Ebool_2ECOND_2E3(tyop_2Esptree_2Espt(A_27a),c_2Earithmetic_2EEVEN_2E1(V3k_2E0),c_2Esptree_2Emk__BN_2E2(A_27a,c_2Esptree_2Edelete_2E2(A_27a,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V3k_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),V4t1_2E0),V5t2_2E0),c_2Esptree_2Emk__BN_2E2(A_27a,V4t1_2E0,c_2Esptree_2Edelete_2E2(A_27a,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V3k_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),V5t2_2E0)))) )
& ! [V6k_2E0: tyop_2Enum_2Enum,V7t1_2E0: tyop_2Esptree_2Espt(A_27a),V8a_2E0: A_27a,V9t2_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Edelete_2E2(A_27a,V6k_2E0,c_2Esptree_2EBS_2E3(A_27a,V7t1_2E0,V8a_2E0,V9t2_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F2_2E0,V6k_2E0),c_2Esptree_2EBN_2E2(A_27a,V7t1_2E0,V9t2_2E0),c_2Ebool_2ECOND_2E3(tyop_2Esptree_2Espt(A_27a),c_2Earithmetic_2EEVEN_2E1(V6k_2E0),c_2Esptree_2Emk__BS_2E3(A_27a,c_2Esptree_2Edelete_2E2(A_27a,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V6k_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),V7t1_2E0),V8a_2E0,V9t2_2E0),c_2Esptree_2Emk__BS_2E3(A_27a,V7t1_2E0,V8a_2E0,c_2Esptree_2Edelete_2E2(A_27a,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V6k_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),V9t2_2E0)))) ) ) ) ) ) ).
tff(thm_2Esptree_2EfromList__def,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))))] :
( ! [V1i_2E0: tyop_2Enum_2Enum,V2t_2E0: tyop_2Esptree_2Espt(A_27a),V3a_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)))),F0_2E0,V1i_2E0),V2t_2E0),V3a_2E0) = c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a),c_2Earithmetic_2E_2B_2E2(V1i_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Esptree_2Einsert_2E3(A_27a,V1i_2E0,V3a_2E0,V2t_2E0)) )
=> ! [V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Esptree_2EfromList_2E1(A_27a,V0l_2E0) = c_2Epair_2ESND_2E1(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a),c_2Elist_2EFOLDL_2E3(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a)),c_2Epair_2EUNCURRY_2E1(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a))),F0_2E0),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a),c_2Enum_2E0_2E0,c_2Esptree_2ELN_2E0(A_27a)),V0l_2E0)) ) ) ).
tff(thm_2Esptree_2Esize__def,axiom,
! [A_27a: $tType] :
( ( c_2Esptree_2Esize_2E1(A_27a,c_2Esptree_2ELN_2E0(A_27a)) = c_2Enum_2E0_2E0 )
& ! [V0a_2E0: A_27a] : ( c_2Esptree_2Esize_2E1(A_27a,c_2Esptree_2ELS_2E1(A_27a,V0a_2E0)) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) )
& ! [V1t1_2E0: tyop_2Esptree_2Espt(A_27a),V2t2_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Esize_2E1(A_27a,c_2Esptree_2EBN_2E2(A_27a,V1t1_2E0,V2t2_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Esptree_2Esize_2E1(A_27a,V1t1_2E0),c_2Esptree_2Esize_2E1(A_27a,V2t2_2E0)) )
& ! [V3t1_2E0: tyop_2Esptree_2Espt(A_27a),V4a_2E0: A_27a,V5t2_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Esize_2E1(A_27a,c_2Esptree_2EBS_2E3(A_27a,V3t1_2E0,V4a_2E0,V5t2_2E0)) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2B_2E2(c_2Esptree_2Esize_2E1(A_27a,V3t1_2E0),c_2Esptree_2Esize_2E1(A_27a,V5t2_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) ) ) ).
tff(thm_2Esptree_2Eunion__def,axiom,
! [A_27a: $tType,F4_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),F7_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))))),F1_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)))),F5_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))))),F8_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))))),F2_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))))),F3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),F6_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)))] :
( ! [V9t1_2E0: tyop_2Esptree_2Espt(A_27a),V10t2_2E0: tyop_2Esptree_2Espt(A_27a),V13t1_27_2E0: tyop_2Esptree_2Espt(A_27a),V14t2_27_2E0: tyop_2Esptree_2Espt(A_27a)] : ( app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),F4_2E0,V9t1_2E0),V10t2_2E0),V13t1_27_2E0),V14t2_27_2E0) = c_2Esptree_2EBN_2E2(A_27a,c_2Esptree_2Eunion_2E2(A_27a,V9t1_2E0,V13t1_27_2E0),c_2Esptree_2Eunion_2E2(A_27a,V10t2_2E0,V14t2_27_2E0)) )
=> ( ! [V9t1_2E0: tyop_2Esptree_2Espt(A_27a),V10t2_2E0: tyop_2Esptree_2Espt(A_27a),V15t1_27_27_2E0: tyop_2Esptree_2Espt(A_27a),V16a_27_27_2E0: A_27a,V17t2_27_27_2E0: tyop_2Esptree_2Espt(A_27a)] : ( app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),F7_2E0,V9t1_2E0),V10t2_2E0),V15t1_27_27_2E0),V16a_27_27_2E0),V17t2_27_27_2E0) = c_2Esptree_2EBS_2E3(A_27a,c_2Esptree_2Eunion_2E2(A_27a,V9t1_2E0,V15t1_27_27_2E0),V16a_27_27_2E0,c_2Esptree_2Eunion_2E2(A_27a,V10t2_2E0,V17t2_27_27_2E0)) )
=> ( ! [V9t1_2E0: tyop_2Esptree_2Espt(A_27a),V10t2_2E0: tyop_2Esptree_2Espt(A_27a),V12a_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))),F1_2E0,V9t1_2E0),V10t2_2E0),V12a_2E0) = c_2Esptree_2EBS_2E3(A_27a,V9t1_2E0,V12a_2E0,V10t2_2E0) )
=> ( ! [V18t1_2E0: tyop_2Esptree_2Espt(A_27a),V19a_2E0: A_27a,V20t2_2E0: tyop_2Esptree_2Espt(A_27a),V23t1_27_2E0: tyop_2Esptree_2Espt(A_27a),V24t2_27_2E0: tyop_2Esptree_2Espt(A_27a)] : ( app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),F5_2E0,V18t1_2E0),V19a_2E0),V20t2_2E0),V23t1_27_2E0),V24t2_27_2E0) = c_2Esptree_2EBS_2E3(A_27a,c_2Esptree_2Eunion_2E2(A_27a,V18t1_2E0,V23t1_27_2E0),V19a_2E0,c_2Esptree_2Eunion_2E2(A_27a,V20t2_2E0,V24t2_27_2E0)) )
=> ( ! [V18t1_2E0: tyop_2Esptree_2Espt(A_27a),V19a_2E0: A_27a,V20t2_2E0: tyop_2Esptree_2Espt(A_27a),V25t1_27_27_2E0: tyop_2Esptree_2Espt(A_27a),V26a_27_27_27_2E0: A_27a,V27t2_27_27_2E0: tyop_2Esptree_2Espt(A_27a)] : ( app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))))),F8_2E0,V18t1_2E0),V19a_2E0),V20t2_2E0),V25t1_27_27_2E0),V26a_27_27_27_2E0),V27t2_27_27_2E0) = c_2Esptree_2EBS_2E3(A_27a,c_2Esptree_2Eunion_2E2(A_27a,V18t1_2E0,V25t1_27_27_2E0),V19a_2E0,c_2Esptree_2Eunion_2E2(A_27a,V20t2_2E0,V27t2_27_27_2E0)) )
=> ( ! [V18t1_2E0: tyop_2Esptree_2Espt(A_27a),V19a_2E0: A_27a,V20t2_2E0: tyop_2Esptree_2Espt(A_27a),V22a_27_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)))),F2_2E0,V18t1_2E0),V19a_2E0),V20t2_2E0),V22a_27_2E0) = c_2Esptree_2EBS_2E3(A_27a,V18t1_2E0,V19a_2E0,V20t2_2E0) )
=> ( ! [V1a_2E0: A_27a,V4t1_2E0: tyop_2Esptree_2Espt(A_27a),V5t2_2E0: tyop_2Esptree_2Espt(A_27a)] : ( app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),F3_2E0,V1a_2E0),V4t1_2E0),V5t2_2E0) = c_2Esptree_2EBS_2E3(A_27a,V4t1_2E0,V1a_2E0,V5t2_2E0) )
=> ( ! [V1a_2E0: A_27a,V6t1_27_2E0: tyop_2Esptree_2Espt(A_27a),V7v4_2E0: A_27a,V8t2_27_2E0: tyop_2Esptree_2Espt(A_27a)] : ( app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),F6_2E0,V1a_2E0),V6t1_27_2E0),V7v4_2E0),V8t2_27_2E0) = c_2Esptree_2EBS_2E3(A_27a,V6t1_27_2E0,V1a_2E0,V8t2_27_2E0) )
=> ( ! [V1a_2E0: A_27a,V3b_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Esptree_2Espt(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),F0_2E0,V1a_2E0),V3b_2E0) = c_2Esptree_2ELS_2E1(A_27a,V1a_2E0) )
=> ( ! [V0t_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Eunion_2E2(A_27a,c_2Esptree_2ELN_2E0(A_27a),V0t_2E0) = V0t_2E0 )
& ! [V1a_2E0: A_27a,V2t_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Eunion_2E2(A_27a,c_2Esptree_2ELS_2E1(A_27a,V1a_2E0),V2t_2E0) = c_2Esptree_2Espt__CASE_2E5(A_27a,tyop_2Esptree_2Espt(A_27a),V2t_2E0,c_2Esptree_2ELS_2E1(A_27a,V1a_2E0),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),F0_2E0,V1a_2E0),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),F3_2E0,V1a_2E0),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),F6_2E0,V1a_2E0)) )
& ! [V9t1_2E0: tyop_2Esptree_2Espt(A_27a),V10t2_2E0: tyop_2Esptree_2Espt(A_27a),V11t_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Eunion_2E2(A_27a,c_2Esptree_2EBN_2E2(A_27a,V9t1_2E0,V10t2_2E0),V11t_2E0) = c_2Esptree_2Espt__CASE_2E5(A_27a,tyop_2Esptree_2Espt(A_27a),V11t_2E0,c_2Esptree_2EBN_2E2(A_27a,V9t1_2E0,V10t2_2E0),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))),F1_2E0,V9t1_2E0),V10t2_2E0),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),F4_2E0,V9t1_2E0),V10t2_2E0),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),F7_2E0,V9t1_2E0),V10t2_2E0)) )
& ! [V18t1_2E0: tyop_2Esptree_2Espt(A_27a),V19a_2E0: A_27a,V20t2_2E0: tyop_2Esptree_2Espt(A_27a),V21t_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Eunion_2E2(A_27a,c_2Esptree_2EBS_2E3(A_27a,V18t1_2E0,V19a_2E0,V20t2_2E0),V21t_2E0) = c_2Esptree_2Espt__CASE_2E5(A_27a,tyop_2Esptree_2Espt(A_27a),V21t_2E0,c_2Esptree_2EBS_2E3(A_27a,V18t1_2E0,V19a_2E0,V20t2_2E0),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)))),F2_2E0,V18t1_2E0),V19a_2E0),V20t2_2E0),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),F5_2E0,V18t1_2E0),V19a_2E0),V20t2_2E0),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))))),F8_2E0,V18t1_2E0),V19a_2E0),V20t2_2E0)) ) ) ) ) ) ) ) ) ) ) ) ).
tff(thm_2Esptree_2Einter__def,axiom,
! [A_27a: $tType,A_27b: $tType,F3_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),F5_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),F4_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),F7_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))))),F8_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))))),F1_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),F6_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),F2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a))),F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)))] :
( ! [V4t1_2E0: tyop_2Esptree_2Espt(A_27b),V5t2_2E0: tyop_2Esptree_2Espt(A_27b)] : ( app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),F3_2E0,V4t1_2E0),V5t2_2E0) = c_2Esptree_2ELN_2E0(A_27a) )
=> ( ! [V18t1_2E0: tyop_2Esptree_2Espt(A_27a),V20t2_2E0: tyop_2Esptree_2Espt(A_27a),V23t1_27_2E0: tyop_2Esptree_2Espt(A_27b),V24t2_27_2E0: tyop_2Esptree_2Espt(A_27b)] : ( app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),F5_2E0,V18t1_2E0),V20t2_2E0),V23t1_27_2E0),V24t2_27_2E0) = c_2Esptree_2Emk__BN_2E2(A_27a,c_2Esptree_2Einter_2E2(A_27a,A_27b,V18t1_2E0,V23t1_27_2E0),c_2Esptree_2Einter_2E2(A_27a,A_27b,V20t2_2E0,V24t2_27_2E0)) )
=> ( ! [V9t1_2E0: tyop_2Esptree_2Espt(A_27a),V10t2_2E0: tyop_2Esptree_2Espt(A_27a),V13t1_27_2E0: tyop_2Esptree_2Espt(A_27b),V14t2_27_2E0: tyop_2Esptree_2Espt(A_27b)] : ( app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),F4_2E0,V9t1_2E0),V10t2_2E0),V13t1_27_2E0),V14t2_27_2E0) = c_2Esptree_2Emk__BN_2E2(A_27a,c_2Esptree_2Einter_2E2(A_27a,A_27b,V9t1_2E0,V13t1_27_2E0),c_2Esptree_2Einter_2E2(A_27a,A_27b,V10t2_2E0,V14t2_27_2E0)) )
=> ( ! [V9t1_2E0: tyop_2Esptree_2Espt(A_27a),V10t2_2E0: tyop_2Esptree_2Espt(A_27a),V15t1_27_27_2E0: tyop_2Esptree_2Espt(A_27b),V16a_27_27_2E0: A_27b,V17t2_27_27_2E0: tyop_2Esptree_2Espt(A_27b)] : ( app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),F7_2E0,V9t1_2E0),V10t2_2E0),V15t1_27_27_2E0),V16a_27_27_2E0),V17t2_27_27_2E0) = c_2Esptree_2Emk__BN_2E2(A_27a,c_2Esptree_2Einter_2E2(A_27a,A_27b,V9t1_2E0,V15t1_27_27_2E0),c_2Esptree_2Einter_2E2(A_27a,A_27b,V10t2_2E0,V17t2_27_27_2E0)) )
=> ( ! [V18t1_2E0: tyop_2Esptree_2Espt(A_27a),V19a_2E0: A_27a,V20t2_2E0: tyop_2Esptree_2Espt(A_27a),V25t1_27_27_2E0: tyop_2Esptree_2Espt(A_27b),V26a_27_27_27_2E0: A_27b,V27t2_27_27_2E0: tyop_2Esptree_2Espt(A_27b)] : ( app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))))),F8_2E0,V18t1_2E0),V19a_2E0),V20t2_2E0),V25t1_27_27_2E0),V26a_27_27_27_2E0),V27t2_27_27_2E0) = c_2Esptree_2Emk__BS_2E3(A_27a,c_2Esptree_2Einter_2E2(A_27a,A_27b,V18t1_2E0,V25t1_27_27_2E0),V19a_2E0,c_2Esptree_2Einter_2E2(A_27a,A_27b,V20t2_2E0,V27t2_27_27_2E0)) )
=> ( ! [V12a_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Esptree_2Espt(A_27a),F1_2E0,V12a_2E0) = c_2Esptree_2ELN_2E0(A_27a) )
=> ( ! [V1a_2E0: A_27a,V6t1_27_2E0: tyop_2Esptree_2Espt(A_27b),V7v4_2E0: A_27b,V8t2_27_2E0: tyop_2Esptree_2Espt(A_27b)] : ( app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),F6_2E0,V1a_2E0),V6t1_27_2E0),V7v4_2E0),V8t2_27_2E0) = c_2Esptree_2ELS_2E1(A_27a,V1a_2E0) )
=> ( ! [V19a_2E0: A_27a,V22a_27_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Esptree_2Espt(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),F2_2E0,V19a_2E0),V22a_27_2E0) = c_2Esptree_2ELS_2E1(A_27a,V19a_2E0) )
=> ( ! [V1a_2E0: A_27a,V3b_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Esptree_2Espt(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),F0_2E0,V1a_2E0),V3b_2E0) = c_2Esptree_2ELS_2E1(A_27a,V1a_2E0) )
=> ( ! [V0t_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Einter_2E2(A_27a,A_27b,c_2Esptree_2ELN_2E0(A_27a),V0t_2E0) = c_2Esptree_2ELN_2E0(A_27a) )
& ! [V1a_2E0: A_27a,V2t_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Einter_2E2(A_27a,A_27b,c_2Esptree_2ELS_2E1(A_27a,V1a_2E0),V2t_2E0) = c_2Esptree_2Espt__CASE_2E5(A_27b,tyop_2Esptree_2Espt(A_27a),V2t_2E0,c_2Esptree_2ELN_2E0(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),F0_2E0,V1a_2E0),F3_2E0,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),F6_2E0,V1a_2E0)) )
& ! [V9t1_2E0: tyop_2Esptree_2Espt(A_27a),V10t2_2E0: tyop_2Esptree_2Espt(A_27a),V11t_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Einter_2E2(A_27a,A_27b,c_2Esptree_2EBN_2E2(A_27a,V9t1_2E0,V10t2_2E0),V11t_2E0) = c_2Esptree_2Espt__CASE_2E5(A_27b,tyop_2Esptree_2Espt(A_27a),V11t_2E0,c_2Esptree_2ELN_2E0(A_27a),F1_2E0,app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),F4_2E0,V9t1_2E0),V10t2_2E0),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),F7_2E0,V9t1_2E0),V10t2_2E0)) )
& ! [V18t1_2E0: tyop_2Esptree_2Espt(A_27a),V19a_2E0: A_27a,V20t2_2E0: tyop_2Esptree_2Espt(A_27a),V21t_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Einter_2E2(A_27a,A_27b,c_2Esptree_2EBS_2E3(A_27a,V18t1_2E0,V19a_2E0,V20t2_2E0),V21t_2E0) = c_2Esptree_2Espt__CASE_2E5(A_27b,tyop_2Esptree_2Espt(A_27a),V21t_2E0,c_2Esptree_2ELN_2E0(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),F2_2E0,V19a_2E0),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),F5_2E0,V18t1_2E0),V20t2_2E0),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))))),F8_2E0,V18t1_2E0),V19a_2E0),V20t2_2E0)) ) ) ) ) ) ) ) ) ) ) ) ).
tff(thm_2Esptree_2Einter__eq__def,axiom,
! [A_27a: $tType,F3_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),F5_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),F4_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),F7_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))))),F1_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),F12_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F8_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))))),F11_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F6_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),F10_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a))),F9_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)))] :
( ! [V4t1_2E0: tyop_2Esptree_2Espt(A_27a),V5t2_2E0: tyop_2Esptree_2Espt(A_27a)] : ( app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),F3_2E0,V4t1_2E0),V5t2_2E0) = c_2Esptree_2ELN_2E0(A_27a) )
=> ( ! [V18t1_2E0: tyop_2Esptree_2Espt(A_27a),V20t2_2E0: tyop_2Esptree_2Espt(A_27a),V23t1_27_2E0: tyop_2Esptree_2Espt(A_27a),V24t2_27_2E0: tyop_2Esptree_2Espt(A_27a)] : ( app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),F5_2E0,V18t1_2E0),V20t2_2E0),V23t1_27_2E0),V24t2_27_2E0) = c_2Esptree_2Emk__BN_2E2(A_27a,c_2Esptree_2Einter__eq_2E2(A_27a,V18t1_2E0,V23t1_27_2E0),c_2Esptree_2Einter__eq_2E2(A_27a,V20t2_2E0,V24t2_27_2E0)) )
=> ( ! [V9t1_2E0: tyop_2Esptree_2Espt(A_27a),V10t2_2E0: tyop_2Esptree_2Espt(A_27a),V13t1_27_2E0: tyop_2Esptree_2Espt(A_27a),V14t2_27_2E0: tyop_2Esptree_2Espt(A_27a)] : ( app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),F4_2E0,V9t1_2E0),V10t2_2E0),V13t1_27_2E0),V14t2_27_2E0) = c_2Esptree_2Emk__BN_2E2(A_27a,c_2Esptree_2Einter__eq_2E2(A_27a,V9t1_2E0,V13t1_27_2E0),c_2Esptree_2Einter__eq_2E2(A_27a,V10t2_2E0,V14t2_27_2E0)) )
=> ( ! [V9t1_2E0: tyop_2Esptree_2Espt(A_27a),V10t2_2E0: tyop_2Esptree_2Espt(A_27a),V15t1_27_27_2E0: tyop_2Esptree_2Espt(A_27a),V16a_27_27_2E0: A_27a,V17t2_27_27_2E0: tyop_2Esptree_2Espt(A_27a)] : ( app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),F7_2E0,V9t1_2E0),V10t2_2E0),V15t1_27_27_2E0),V16a_27_27_2E0),V17t2_27_27_2E0) = c_2Esptree_2Emk__BN_2E2(A_27a,c_2Esptree_2Einter__eq_2E2(A_27a,V9t1_2E0,V15t1_27_27_2E0),c_2Esptree_2Einter__eq_2E2(A_27a,V10t2_2E0,V17t2_27_27_2E0)) )
=> ( ! [V12a_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Esptree_2Espt(A_27a),F1_2E0,V12a_2E0) = c_2Esptree_2ELN_2E0(A_27a) )
=> ( ! [V26a_27_27_27_2E0: A_27a,V19a_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F12_2E0,V26a_27_27_27_2E0),V19a_2E0))
<=> ( V26a_27_27_27_2E0 = V19a_2E0 ) )
=> ( ! [V19a_2E0: A_27a,V18t1_2E0: tyop_2Esptree_2Espt(A_27a),V20t2_2E0: tyop_2Esptree_2Espt(A_27a),V25t1_27_27_2E0: tyop_2Esptree_2Espt(A_27a),V26a_27_27_27_2E0: A_27a,V27t2_27_27_2E0: tyop_2Esptree_2Espt(A_27a)] : ( app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))))),F8_2E0,V19a_2E0),V18t1_2E0),V20t2_2E0),V25t1_27_27_2E0),V26a_27_27_27_2E0),V27t2_27_27_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Esptree_2Espt(A_27a),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F12_2E0,V26a_27_27_27_2E0),V19a_2E0),c_2Esptree_2Emk__BS_2E3(A_27a,c_2Esptree_2Einter__eq_2E2(A_27a,V18t1_2E0,V25t1_27_27_2E0),V19a_2E0,c_2Esptree_2Einter__eq_2E2(A_27a,V20t2_2E0,V27t2_27_27_2E0)),c_2Esptree_2Emk__BN_2E2(A_27a,c_2Esptree_2Einter__eq_2E2(A_27a,V18t1_2E0,V25t1_27_27_2E0),c_2Esptree_2Einter__eq_2E2(A_27a,V20t2_2E0,V27t2_27_27_2E0))) )
=> ( ! [V1a_2E0: A_27a,V7b_27_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F11_2E0,V1a_2E0),V7b_27_2E0))
<=> ( V1a_2E0 = V7b_27_2E0 ) )
=> ( ! [V1a_2E0: A_27a,V6t1_27_2E0: tyop_2Esptree_2Espt(A_27a),V7b_27_2E0: A_27a,V8t2_27_2E0: tyop_2Esptree_2Espt(A_27a)] : ( app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),F6_2E0,V1a_2E0),V6t1_27_2E0),V7b_27_2E0),V8t2_27_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Esptree_2Espt(A_27a),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F11_2E0,V1a_2E0),V7b_27_2E0),c_2Esptree_2ELS_2E1(A_27a,V1a_2E0),c_2Esptree_2ELN_2E0(A_27a)) )
=> ( ! [V1a_2E0: A_27a,V3b_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F10_2E0,V1a_2E0),V3b_2E0))
<=> ( V1a_2E0 = V3b_2E0 ) )
=> ( ! [V1a_2E0: A_27a,V3b_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Esptree_2Espt(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),F0_2E0,V1a_2E0),V3b_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Esptree_2Espt(A_27a),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F10_2E0,V1a_2E0),V3b_2E0),c_2Esptree_2ELS_2E1(A_27a,V1a_2E0),c_2Esptree_2ELN_2E0(A_27a)) )
=> ( ! [V22a_27_2E0: A_27a,V19a_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F9_2E0,V22a_27_2E0),V19a_2E0))
<=> ( V22a_27_2E0 = V19a_2E0 ) )
=> ( ! [V19a_2E0: A_27a,V22a_27_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Esptree_2Espt(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),F2_2E0,V19a_2E0),V22a_27_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Esptree_2Espt(A_27a),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),F9_2E0,V22a_27_2E0),V19a_2E0),c_2Esptree_2ELS_2E1(A_27a,V19a_2E0),c_2Esptree_2ELN_2E0(A_27a)) )
=> ( ! [V0t_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Einter__eq_2E2(A_27a,c_2Esptree_2ELN_2E0(A_27a),V0t_2E0) = c_2Esptree_2ELN_2E0(A_27a) )
& ! [V1a_2E0: A_27a,V2t_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Einter__eq_2E2(A_27a,c_2Esptree_2ELS_2E1(A_27a,V1a_2E0),V2t_2E0) = c_2Esptree_2Espt__CASE_2E5(A_27a,tyop_2Esptree_2Espt(A_27a),V2t_2E0,c_2Esptree_2ELN_2E0(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),F0_2E0,V1a_2E0),F3_2E0,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),F6_2E0,V1a_2E0)) )
& ! [V9t1_2E0: tyop_2Esptree_2Espt(A_27a),V10t2_2E0: tyop_2Esptree_2Espt(A_27a),V11t_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Einter__eq_2E2(A_27a,c_2Esptree_2EBN_2E2(A_27a,V9t1_2E0,V10t2_2E0),V11t_2E0) = c_2Esptree_2Espt__CASE_2E5(A_27a,tyop_2Esptree_2Espt(A_27a),V11t_2E0,c_2Esptree_2ELN_2E0(A_27a),F1_2E0,app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),F4_2E0,V9t1_2E0),V10t2_2E0),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),F7_2E0,V9t1_2E0),V10t2_2E0)) )
& ! [V18t1_2E0: tyop_2Esptree_2Espt(A_27a),V19a_2E0: A_27a,V20t2_2E0: tyop_2Esptree_2Espt(A_27a),V21t_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Einter__eq_2E2(A_27a,c_2Esptree_2EBS_2E3(A_27a,V18t1_2E0,V19a_2E0,V20t2_2E0),V21t_2E0) = c_2Esptree_2Espt__CASE_2E5(A_27a,tyop_2Esptree_2Espt(A_27a),V21t_2E0,c_2Esptree_2ELN_2E0(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),F2_2E0,V19a_2E0),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),F5_2E0,V18t1_2E0),V20t2_2E0),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))))),F8_2E0,V19a_2E0),V18t1_2E0),V20t2_2E0)) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ) ).
tff(thm_2Esptree_2Edifference__def,axiom,
! [A_27a: $tType,A_27b: $tType,F6_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),F4_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),F8_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))))),F7_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))))),F2_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)))),F1_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)))),F5_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))))),F0_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),F3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))] :
( ! [V6t1_27_2E0: tyop_2Esptree_2Espt(A_27b),V7b_27_2E0: A_27b,V8t2_27_2E0: tyop_2Esptree_2Espt(A_27b)] : ( app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),F6_2E0,V6t1_27_2E0),V7b_27_2E0),V8t2_27_2E0) = c_2Esptree_2ELN_2E0(A_27a) )
=> ( ! [V9t1_2E0: tyop_2Esptree_2Espt(A_27a),V10t2_2E0: tyop_2Esptree_2Espt(A_27a),V13t1_27_2E0: tyop_2Esptree_2Espt(A_27b),V14t2_27_2E0: tyop_2Esptree_2Espt(A_27b)] : ( app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),F4_2E0,V9t1_2E0),V10t2_2E0),V13t1_27_2E0),V14t2_27_2E0) = c_2Esptree_2Emk__BN_2E2(A_27a,c_2Esptree_2Edifference_2E2(A_27a,A_27b,V9t1_2E0,V13t1_27_2E0),c_2Esptree_2Edifference_2E2(A_27a,A_27b,V10t2_2E0,V14t2_27_2E0)) )
=> ( ! [V18t1_2E0: tyop_2Esptree_2Espt(A_27a),V20t2_2E0: tyop_2Esptree_2Espt(A_27a),V25t1_27_27_2E0: tyop_2Esptree_2Espt(A_27b),V26a_27_27_27_2E0: A_27b,V27t2_27_27_2E0: tyop_2Esptree_2Espt(A_27b)] : ( app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),F8_2E0,V18t1_2E0),V20t2_2E0),V25t1_27_27_2E0),V26a_27_27_27_2E0),V27t2_27_27_2E0) = c_2Esptree_2Emk__BN_2E2(A_27a,c_2Esptree_2Edifference_2E2(A_27a,A_27b,V18t1_2E0,V25t1_27_27_2E0),c_2Esptree_2Edifference_2E2(A_27a,A_27b,V20t2_2E0,V27t2_27_27_2E0)) )
=> ( ! [V9t1_2E0: tyop_2Esptree_2Espt(A_27a),V10t2_2E0: tyop_2Esptree_2Espt(A_27a),V15t1_27_27_2E0: tyop_2Esptree_2Espt(A_27b),V16a_27_27_2E0: A_27b,V17t2_27_27_2E0: tyop_2Esptree_2Espt(A_27b)] : ( app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a),app_2E2(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),F7_2E0,V9t1_2E0),V10t2_2E0),V15t1_27_27_2E0),V16a_27_27_2E0),V17t2_27_27_2E0) = c_2Esptree_2Emk__BN_2E2(A_27a,c_2Esptree_2Edifference_2E2(A_27a,A_27b,V9t1_2E0,V15t1_27_27_2E0),c_2Esptree_2Edifference_2E2(A_27a,A_27b,V10t2_2E0,V17t2_27_27_2E0)) )
=> ( ! [V18t1_2E0: tyop_2Esptree_2Espt(A_27a),V20t2_2E0: tyop_2Esptree_2Espt(A_27a),V22a_27_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a))),F2_2E0,V18t1_2E0),V20t2_2E0),V22a_27_2E0) = c_2Esptree_2EBN_2E2(A_27a,V18t1_2E0,V20t2_2E0) )
=> ( ! [V9t1_2E0: tyop_2Esptree_2Espt(A_27a),V10t2_2E0: tyop_2Esptree_2Espt(A_27a),V12a_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a))),F1_2E0,V9t1_2E0),V10t2_2E0),V12a_2E0) = c_2Esptree_2EBN_2E2(A_27a,V9t1_2E0,V10t2_2E0) )
=> ( ! [V18t1_2E0: tyop_2Esptree_2Espt(A_27a),V19a_2E0: A_27a,V20t2_2E0: tyop_2Esptree_2Espt(A_27a),V23t1_27_2E0: tyop_2Esptree_2Espt(A_27b),V24t2_27_2E0: tyop_2Esptree_2Espt(A_27b)] : ( app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),F5_2E0,V18t1_2E0),V19a_2E0),V20t2_2E0),V23t1_27_2E0),V24t2_27_2E0) = c_2Esptree_2Emk__BS_2E3(A_27a,c_2Esptree_2Edifference_2E2(A_27a,A_27b,V18t1_2E0,V23t1_27_2E0),V19a_2E0,c_2Esptree_2Edifference_2E2(A_27a,A_27b,V20t2_2E0,V24t2_27_2E0)) )
=> ( ! [V3b_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Esptree_2Espt(A_27a),F0_2E0,V3b_2E0) = c_2Esptree_2ELN_2E0(A_27a) )
=> ( ! [V1a_2E0: A_27a,V4t1_2E0: tyop_2Esptree_2Espt(A_27b),V5t2_2E0: tyop_2Esptree_2Espt(A_27b)] : ( app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),F3_2E0,V1a_2E0),V4t1_2E0),V5t2_2E0) = c_2Esptree_2ELS_2E1(A_27a,V1a_2E0) )
=> ( ! [V0t_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Edifference_2E2(A_27a,A_27b,c_2Esptree_2ELN_2E0(A_27a),V0t_2E0) = c_2Esptree_2ELN_2E0(A_27a) )
& ! [V1a_2E0: A_27a,V2t_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Edifference_2E2(A_27a,A_27b,c_2Esptree_2ELS_2E1(A_27a,V1a_2E0),V2t_2E0) = c_2Esptree_2Espt__CASE_2E5(A_27b,tyop_2Esptree_2Espt(A_27a),V2t_2E0,c_2Esptree_2ELS_2E1(A_27a,V1a_2E0),F0_2E0,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),F3_2E0,V1a_2E0),F6_2E0) )
& ! [V9t1_2E0: tyop_2Esptree_2Espt(A_27a),V10t2_2E0: tyop_2Esptree_2Espt(A_27a),V11t_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Edifference_2E2(A_27a,A_27b,c_2Esptree_2EBN_2E2(A_27a,V9t1_2E0,V10t2_2E0),V11t_2E0) = c_2Esptree_2Espt__CASE_2E5(A_27b,tyop_2Esptree_2Espt(A_27a),V11t_2E0,c_2Esptree_2EBN_2E2(A_27a,V9t1_2E0,V10t2_2E0),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a))),F1_2E0,V9t1_2E0),V10t2_2E0),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),F4_2E0,V9t1_2E0),V10t2_2E0),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),F7_2E0,V9t1_2E0),V10t2_2E0)) )
& ! [V18t1_2E0: tyop_2Esptree_2Espt(A_27a),V19a_2E0: A_27a,V20t2_2E0: tyop_2Esptree_2Espt(A_27a),V21t_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Edifference_2E2(A_27a,A_27b,c_2Esptree_2EBS_2E3(A_27a,V18t1_2E0,V19a_2E0,V20t2_2E0),V21t_2E0) = c_2Esptree_2Espt__CASE_2E5(A_27b,tyop_2Esptree_2Espt(A_27a),V21t_2E0,c_2Esptree_2EBS_2E3(A_27a,V18t1_2E0,V19a_2E0,V20t2_2E0),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a)),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Esptree_2Espt(A_27a))),F2_2E0,V18t1_2E0),V20t2_2E0),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),F5_2E0,V18t1_2E0),V19a_2E0),V20t2_2E0),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a)))),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Esptree_2Espt(A_27a))))),F8_2E0,V18t1_2E0),V20t2_2E0)) ) ) ) ) ) ) ) ) ) ) ) ).
tff(thm_2Esptree_2Elrnext__primitive__def,axiom,
! [F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool)] :
( ! [V3a_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F2_2E0,V3a_2E0))
<=> ( V3a_2E0 = c_2Enum_2E0_2E0 ) )
=> ( ! [V2lrnext_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),V3a_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),F1_2E0,V2lrnext_2E0),V3a_2E0) = c_2Ecombin_2EI_2E1(tyop_2Enum_2Enum,c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F2_2E0,V3a_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,V2lrnext_2E0,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V3a_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))))) )
=> ( ! [V0R_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
( p(app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),tyop_2Emin_2Ebool,F0_2E0,V0R_2E0))
<=> ( p(c_2Erelation_2EWF_2E1(tyop_2Enum_2Enum,V0R_2E0))
& ! [V1n_2E0: tyop_2Enum_2Enum] :
( ( V1n_2E0 != c_2Enum_2E0_2E0 )
=> p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0R_2E0,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V1n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))),V1n_2E0)) ) ) )
=> ( c_2Esptree_2Elrnext_2E0 = c_2Erelation_2EWFREC_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,c_2Emin_2E_40_2E1(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),F0_2E0),F1_2E0) ) ) ) ) ).
tff(thm_2Esptree_2Edomain__def,axiom,
! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),F3_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)] :
( ! [V8n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,F1_2E0,V8n_2E0) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V8n_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))) )
=> ( ! [V3n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,F0_2E0,V3n_2E0) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V3n_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))) )
=> ( ! [V9n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,F3_2E0,V9n_2E0) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V9n_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) )
=> ( ! [V4n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,F2_2E0,V4n_2E0) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),V4n_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))) )
=> ( ( c_2Esptree_2Edomain_2E1(A_27a,c_2Esptree_2ELN_2E0(A_27a)) = c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum) )
& ! [V0v0_2E0: A_27a] : ( c_2Esptree_2Edomain_2E1(A_27a,c_2Esptree_2ELS_2E1(A_27a,V0v0_2E0)) = c_2Epred__set_2EINSERT_2E2(tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum)) )
& ! [V1t1_2E0: tyop_2Esptree_2Espt(A_27a),V2t2_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Edomain_2E1(A_27a,c_2Esptree_2EBN_2E2(A_27a,V1t1_2E0,V2t2_2E0)) = c_2Epred__set_2EUNION_2E2(tyop_2Enum_2Enum,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,F0_2E0,c_2Esptree_2Edomain_2E1(A_27a,V1t1_2E0)),c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,F2_2E0,c_2Esptree_2Edomain_2E1(A_27a,V2t2_2E0))) )
& ! [V5t1_2E0: tyop_2Esptree_2Espt(A_27a),V6v1_2E0: A_27a,V7t2_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Edomain_2E1(A_27a,c_2Esptree_2EBS_2E3(A_27a,V5t1_2E0,V6v1_2E0,V7t2_2E0)) = c_2Epred__set_2EUNION_2E2(tyop_2Enum_2Enum,c_2Epred__set_2EUNION_2E2(tyop_2Enum_2Enum,c_2Epred__set_2EINSERT_2E2(tyop_2Enum_2Enum,c_2Enum_2E0_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum)),c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,F1_2E0,c_2Esptree_2Edomain_2E1(A_27a,V5t1_2E0))),c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,F3_2E0,c_2Esptree_2Edomain_2E1(A_27a,V7t2_2E0))) ) ) ) ) ) ) ).
tff(thm_2Esptree_2Espt__fold__def,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),V1acc_2E0: A_27a] : ( c_2Esptree_2Espt__fold_2E3(A_27a,A_27b,V0f_2E0,V1acc_2E0,c_2Esptree_2ELN_2E0(A_27b)) = V1acc_2E0 )
& ! [V2f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),V3acc_2E0: A_27a,V4a_2E0: A_27b] : ( c_2Esptree_2Espt__fold_2E3(A_27a,A_27b,V2f_2E0,V3acc_2E0,c_2Esptree_2ELS_2E1(A_27b,V4a_2E0)) = app_2E2(A_27a,A_27a,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,A_27a),V2f_2E0,V4a_2E0),V3acc_2E0) )
& ! [V5f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),V6acc_2E0: A_27a,V7t1_2E0: tyop_2Esptree_2Espt(A_27b),V8t2_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Espt__fold_2E3(A_27a,A_27b,V5f_2E0,V6acc_2E0,c_2Esptree_2EBN_2E2(A_27b,V7t1_2E0,V8t2_2E0)) = c_2Esptree_2Espt__fold_2E3(A_27a,A_27b,V5f_2E0,c_2Esptree_2Espt__fold_2E3(A_27a,A_27b,V5f_2E0,V6acc_2E0,V7t1_2E0),V8t2_2E0) )
& ! [V9f_2E0: tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27a,A_27a)),V10acc_2E0: A_27a,V11t1_2E0: tyop_2Esptree_2Espt(A_27b),V12a_2E0: A_27b,V13t2_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Espt__fold_2E3(A_27a,A_27b,V9f_2E0,V10acc_2E0,c_2Esptree_2EBS_2E3(A_27b,V11t1_2E0,V12a_2E0,V13t2_2E0)) = c_2Esptree_2Espt__fold_2E3(A_27a,A_27b,V9f_2E0,app_2E2(A_27a,A_27a,app_2E2(A_27b,tyop_2Emin_2Efun(A_27a,A_27a),V9f_2E0,V12a_2E0),c_2Esptree_2Espt__fold_2E3(A_27a,A_27b,V9f_2E0,V10acc_2E0,V11t1_2E0)),V13t2_2E0) ) ) ).
tff(thm_2Esptree_2Elist__to__num__set__def,axiom,
( ( c_2Esptree_2Elist__to__num__set_2E1(c_2Elist_2ENIL_2E0(tyop_2Enum_2Enum)) = c_2Esptree_2ELN_2E0(tyop_2Eone_2Eone) )
& ! [V0n_2E0: tyop_2Enum_2Enum,V1ns_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Esptree_2Elist__to__num__set_2E1(c_2Elist_2ECONS_2E2(tyop_2Enum_2Enum,V0n_2E0,V1ns_2E0)) = c_2Esptree_2Einsert_2E3(tyop_2Eone_2Eone,V0n_2E0,c_2Eone_2Eone_2E0,c_2Esptree_2Elist__to__num__set_2E1(V1ns_2E0)) ) ) ).
tff(thm_2Esptree_2Elist__insert__def,axiom,
( ! [V0t_2E0: tyop_2Esptree_2Espt(tyop_2Eone_2Eone)] : ( c_2Esptree_2Elist__insert_2E2(c_2Elist_2ENIL_2E0(tyop_2Enum_2Enum),V0t_2E0) = V0t_2E0 )
& ! [V1n_2E0: tyop_2Enum_2Enum,V2ns_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum),V3t_2E0: tyop_2Esptree_2Espt(tyop_2Eone_2Eone)] : ( c_2Esptree_2Elist__insert_2E2(c_2Elist_2ECONS_2E2(tyop_2Enum_2Enum,V1n_2E0,V2ns_2E0),V3t_2E0) = c_2Esptree_2Elist__insert_2E2(V2ns_2E0,c_2Esptree_2Einsert_2E3(tyop_2Eone_2Eone,V1n_2E0,c_2Eone_2Eone_2E0,V3t_2E0)) ) ) ).
tff(thm_2Esptree_2Elookup__fromList__outside,axiom,
! [A_27a: $tType,V0args_2E0: tyop_2Elist_2Elist(A_27a),V1k_2E0: tyop_2Enum_2Enum] :
( p(c_2Earithmetic_2E_3C_3D_2E2(c_2Elist_2ELENGTH_2E1(A_27a,V0args_2E0),V1k_2E0))
=> ( c_2Esptree_2Elookup_2E2(A_27a,V1k_2E0,c_2Esptree_2EfromList_2E1(A_27a,V0args_2E0)) = c_2Eoption_2ENONE_2E0(A_27a) ) ) ).
tff(thm_2Esptree_2Esize__delete,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool))] :
( ! [V0n_2E0: tyop_2Enum_2Enum,V1t_2E0: tyop_2Esptree_2Espt(A_27a)] :
( p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),F0_2E0,V0n_2E0),V1t_2E0))
<=> ( c_2Esptree_2Elookup_2E2(A_27a,V0n_2E0,V1t_2E0) = c_2Eoption_2ENONE_2E0(A_27a) ) )
=> ! [V0n_2E0: tyop_2Enum_2Enum,V1t_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Esize_2E1(A_27a,c_2Esptree_2Edelete_2E2(A_27a,V0n_2E0,V1t_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),F0_2E0,V0n_2E0),V1t_2E0),c_2Esptree_2Esize_2E1(A_27a,V1t_2E0),c_2Earithmetic_2E_2D_2E2(c_2Esptree_2Esize_2E1(A_27a,V1t_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) ) ) ).
tff(thm_2Esptree_2Edelete__fail,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1t_2E0: tyop_2Esptree_2Espt(A_27a)] :
( p(c_2Esptree_2Ewf_2E1(A_27a,V1t_2E0))
=> ( ~ p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V0n_2E0,c_2Esptree_2Edomain_2E1(A_27a,V1t_2E0)))
<=> ( c_2Esptree_2Edelete_2E2(A_27a,V0n_2E0,V1t_2E0) = V1t_2E0 ) ) ) ).
tff(thm_2Esptree_2Ewf__difference,axiom,
! [A_27a: $tType,A_27b: $tType,V0t1_2E0: tyop_2Esptree_2Espt(A_27a),V1t2_2E0: tyop_2Esptree_2Espt(A_27b)] :
( ( p(c_2Esptree_2Ewf_2E1(A_27a,V0t1_2E0))
& p(c_2Esptree_2Ewf_2E1(A_27b,V1t2_2E0)) )
=> p(c_2Esptree_2Ewf_2E1(A_27a,c_2Esptree_2Edifference_2E2(A_27a,A_27b,V0t1_2E0,V1t2_2E0))) ) ).
tff(thm_2Esptree_2Edifference__sub,axiom,
! [A_27a: $tType,A_27b: $tType,V0b_2E0: tyop_2Esptree_2Espt(A_27b),V1a_2E0: tyop_2Esptree_2Espt(A_27a)] :
( ( c_2Esptree_2Edifference_2E2(A_27a,A_27b,V1a_2E0,V0b_2E0) = c_2Esptree_2ELN_2E0(A_27a) )
=> p(c_2Epred__set_2ESUBSET_2E2(tyop_2Enum_2Enum,c_2Esptree_2Edomain_2E1(A_27a,V1a_2E0),c_2Esptree_2Edomain_2E1(A_27b,V0b_2E0))) ) ).
tff(thm_2Esptree_2Eunion__num__set__sym,axiom,
! [V0t1_2E0: tyop_2Esptree_2Espt(tyop_2Eone_2Eone),V1t2_2E0: tyop_2Esptree_2Espt(tyop_2Eone_2Eone)] : ( c_2Esptree_2Eunion_2E2(tyop_2Eone_2Eone,V0t1_2E0,V1t2_2E0) = c_2Esptree_2Eunion_2E2(tyop_2Eone_2Eone,V1t2_2E0,V0t1_2E0) ) ).
tff(thm_2Esptree_2Enum__set__domain__eq,axiom,
! [V0t1_2E0: tyop_2Esptree_2Espt(tyop_2Eone_2Eone),V1t2_2E0: tyop_2Esptree_2Espt(tyop_2Eone_2Eone)] :
( ( p(c_2Esptree_2Ewf_2E1(tyop_2Eone_2Eone,V0t1_2E0))
& p(c_2Esptree_2Ewf_2E1(tyop_2Eone_2Eone,V1t2_2E0)) )
=> ( ( c_2Esptree_2Edomain_2E1(tyop_2Eone_2Eone,V0t1_2E0) = c_2Esptree_2Edomain_2E1(tyop_2Eone_2Eone,V1t2_2E0) )
<=> ( V0t1_2E0 = V1t2_2E0 ) ) ) ).
tff(thm_2Esptree_2Esize__domain,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Esize_2E1(A_27a,V0t_2E0) = c_2Epred__set_2ECARD_2E1(tyop_2Enum_2Enum,c_2Esptree_2Edomain_2E1(A_27a,V0t_2E0)) ) ).
tff(thm_2Esptree_2Edomain__mapi,axiom,
! [A_27a: $tType,A_27b: $tType,V0pt_2E0: tyop_2Esptree_2Espt(A_27b),V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a))] : ( c_2Esptree_2Edomain_2E1(A_27a,c_2Esptree_2Emapi_2E2(A_27a,A_27b,V1f_2E0,V0pt_2E0)) = c_2Esptree_2Edomain_2E1(A_27b,V0pt_2E0) ) ).
tff(thm_2Esptree_2Emapi__Alist,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))] :
( ! [V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),V2kv_2E0: tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b)] : ( app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),F0_2E0,V1f_2E0),V2kv_2E0) = c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,A_27a,c_2Epair_2EFST_2E1(tyop_2Enum_2Enum,A_27b,V2kv_2E0),app_2E2(A_27b,A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a),V1f_2E0,c_2Epair_2EFST_2E1(tyop_2Enum_2Enum,A_27b,V2kv_2E0)),c_2Epair_2ESND_2E1(tyop_2Enum_2Enum,A_27b,V2kv_2E0))) )
=> ! [V0pt_2E0: tyop_2Esptree_2Espt(A_27b),V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a))] : ( c_2Esptree_2Emapi_2E2(A_27a,A_27b,V1f_2E0,V0pt_2E0) = c_2Esptree_2EfromAList_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a)),tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),F0_2E0,V1f_2E0),c_2Esptree_2EtoAList_2E1(A_27b,V0pt_2E0))) ) ) ).
tff(thm_2Esptree_2EMAP__foldi,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))),F1_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)))))] :
( ! [V4k_2E0: tyop_2Enum_2Enum,V5v_2E0: A_27a,V6a_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))] : ( app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)))),F0_2E0,V4k_2E0),V5v_2E0),V6a_2E0) = c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,A_27a,V4k_2E0,V5v_2E0),V6a_2E0) )
=> ( ! [V1f_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27b),V7k_2E0: tyop_2Enum_2Enum,V8v_2E0: A_27a,V9a_2E0: tyop_2Elist_2Elist(A_27b)] : ( app_2E2(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b))),app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)))),F1_2E0,V1f_2E0),V7k_2E0),V8v_2E0),V9a_2E0) = c_2Elist_2ECONS_2E2(A_27b,app_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27b,V1f_2E0,c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,A_27a,V7k_2E0,V8v_2E0)),V9a_2E0) )
=> ! [V0pt_2E0: tyop_2Esptree_2Espt(A_27a),V1f_2E0: tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27b),V2n_2E0: tyop_2Enum_2Enum,V3acc_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))] : ( c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27b,V1f_2E0,c_2Esptree_2Efoldi_2E4(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),A_27a,F0_2E0,V2n_2E0,V3acc_2E0,V0pt_2E0)) = c_2Esptree_2Efoldi_2E4(tyop_2Elist_2Elist(A_27b),A_27a,app_2E2(tyop_2Emin_2Efun(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27b),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Elist_2Elist(A_27b),tyop_2Elist_2Elist(A_27b)))),F1_2E0,V1f_2E0),V2n_2E0,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27b,V1f_2E0,V3acc_2E0),V0pt_2E0) ) ) ) ).
tff(thm_2Esptree_2Elookup__mk__BN,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( ! [V2i_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V2i_2E0))
<=> ( V2i_2E0 = c_2Enum_2E0_2E0 ) )
=> ! [V0t2_2E0: tyop_2Esptree_2Espt(A_27a),V1t1_2E0: tyop_2Esptree_2Espt(A_27a),V2i_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Elookup_2E2(A_27a,V2i_2E0,c_2Esptree_2Emk__BN_2E2(A_27a,V1t1_2E0,V0t2_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V2i_2E0),c_2Eoption_2ENONE_2E0(A_27a),c_2Esptree_2Elookup_2E2(A_27a,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V2i_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Ebool_2ECOND_2E3(tyop_2Esptree_2Espt(A_27a),c_2Earithmetic_2EEVEN_2E1(V2i_2E0),V1t1_2E0,V0t2_2E0))) ) ) ).
tff(thm_2Esptree_2Ewf__mapi,axiom,
! [A_27a: $tType,A_27b: $tType,V0pt_2E0: tyop_2Esptree_2Espt(A_27b),V1f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a))] : p(c_2Esptree_2Ewf_2E1(A_27a,c_2Esptree_2Emapi_2E2(A_27a,A_27b,V1f_2E0,V0pt_2E0))) ).
tff(thm_2Esptree_2Ewf__mk__BS,axiom,
! [A_27a: $tType,V0t2_2E0: tyop_2Esptree_2Espt(A_27a),V1t1_2E0: tyop_2Esptree_2Espt(A_27a),V2a_2E0: A_27a] :
( ( p(c_2Esptree_2Ewf_2E1(A_27a,V1t1_2E0))
& p(c_2Esptree_2Ewf_2E1(A_27a,V0t2_2E0)) )
=> p(c_2Esptree_2Ewf_2E1(A_27a,c_2Esptree_2Emk__BS_2E3(A_27a,V1t1_2E0,V2a_2E0,V0t2_2E0))) ) ).
tff(thm_2Esptree_2Ewf__mk__BN,axiom,
! [A_27a: $tType,V0t2_2E0: tyop_2Esptree_2Espt(A_27a),V1t1_2E0: tyop_2Esptree_2Espt(A_27a)] :
( ( p(c_2Esptree_2Ewf_2E1(A_27a,V1t1_2E0))
& p(c_2Esptree_2Ewf_2E1(A_27a,V0t2_2E0)) )
=> p(c_2Esptree_2Ewf_2E1(A_27a,c_2Esptree_2Emk__BN_2E2(A_27a,V1t1_2E0,V0t2_2E0))) ) ).
tff(thm_2Esptree_2Ewf__filter__v,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Esptree_2Espt(A_27a),V1f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] :
( p(c_2Esptree_2Ewf_2E1(A_27a,V0t_2E0))
=> p(c_2Esptree_2Ewf_2E1(A_27a,c_2Esptree_2Efilter__v_2E2(A_27a,V1f_2E0,V0t_2E0))) ) ).
tff(thm_2Esptree_2Elookup__filter__v,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)))] :
( ! [V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),V3v_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),F0_2E0,V2f_2E0),V3v_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),app_2E2(A_27a,tyop_2Emin_2Ebool,V2f_2E0,V3v_2E0),c_2Eoption_2ESOME_2E1(A_27a,V3v_2E0),c_2Eoption_2ENONE_2E0(A_27a)) )
=> ! [V0k_2E0: tyop_2Enum_2Enum,V1t_2E0: tyop_2Esptree_2Espt(A_27a),V2f_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)] : ( c_2Esptree_2Elookup_2E2(A_27a,V0k_2E0,c_2Esptree_2Efilter__v_2E2(A_27a,V2f_2E0,V1t_2E0)) = c_2Eoption_2Eoption__CASE_2E3(A_27a,tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(A_27a,V0k_2E0,V1t_2E0),c_2Eoption_2ENONE_2E0(A_27a),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),F0_2E0,V2f_2E0)) ) ) ).
tff(thm_2Esptree_2Esubspt__LN,axiom,
! [A_27a: $tType,V0sp_2E0: tyop_2Esptree_2Espt(A_27a)] :
( ( c_2Esptree_2Esubspt_2E2(A_27a,c_2Esptree_2ELN_2E0(A_27a),V0sp_2E0) = c_2Ebool_2ET_2E0 )
& ( p(c_2Esptree_2Esubspt_2E2(A_27a,V0sp_2E0,c_2Esptree_2ELN_2E0(A_27a)))
<=> ( c_2Esptree_2Edomain_2E1(A_27a,V0sp_2E0) = c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum) ) ) ) ).
tff(thm_2Esptree_2Esubspt__trans,axiom,
! [A_27a: $tType,V0sp3_2E0: tyop_2Esptree_2Espt(A_27a),V1sp2_2E0: tyop_2Esptree_2Espt(A_27a),V2sp1_2E0: tyop_2Esptree_2Espt(A_27a)] :
( ( p(c_2Esptree_2Esubspt_2E2(A_27a,V2sp1_2E0,V1sp2_2E0))
& p(c_2Esptree_2Esubspt_2E2(A_27a,V1sp2_2E0,V0sp3_2E0)) )
=> p(c_2Esptree_2Esubspt_2E2(A_27a,V2sp1_2E0,V0sp3_2E0)) ) ).
tff(thm_2Esptree_2Esubspt__refl,axiom,
! [A_27a: $tType,V0sp_2E0: tyop_2Esptree_2Espt(A_27a)] : p(c_2Esptree_2Esubspt_2E2(A_27a,V0sp_2E0,V0sp_2E0)) ).
tff(thm_2Esptree_2Esubspt__def,axiom,
! [A_27a: $tType,V0sp1_2E0: tyop_2Esptree_2Espt(A_27a),V1sp2_2E0: tyop_2Esptree_2Espt(A_27a)] :
( p(c_2Esptree_2Esubspt_2E2(A_27a,V0sp1_2E0,V1sp2_2E0))
<=> ! [V2k_2E0: tyop_2Enum_2Enum] :
( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V2k_2E0,c_2Esptree_2Edomain_2E1(A_27a,V0sp1_2E0)))
=> ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V2k_2E0,c_2Esptree_2Edomain_2E1(A_27a,V1sp2_2E0)))
& ( c_2Esptree_2Elookup_2E2(A_27a,V2k_2E0,V1sp2_2E0) = c_2Esptree_2Elookup_2E2(A_27a,V2k_2E0,V0sp1_2E0) ) ) ) ) ).
tff(thm_2Esptree_2Espt__center__def,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1v2_2E0: tyop_2Esptree_2Espt(A_27a),V2v1_2E0: tyop_2Esptree_2Espt(A_27a),V3t2_2E0: tyop_2Esptree_2Espt(A_27a),V4t1_2E0: tyop_2Esptree_2Espt(A_27a)] :
( ( c_2Esptree_2Espt__center_2E1(A_27a,c_2Esptree_2ELS_2E1(A_27a,V0x_2E0)) = c_2Eoption_2ESOME_2E1(A_27a,V0x_2E0) )
& ( c_2Esptree_2Espt__center_2E1(A_27a,c_2Esptree_2EBS_2E3(A_27a,V4t1_2E0,V0x_2E0,V3t2_2E0)) = c_2Eoption_2ESOME_2E1(A_27a,V0x_2E0) )
& ( c_2Esptree_2Espt__center_2E1(A_27a,c_2Esptree_2ELN_2E0(A_27a)) = c_2Eoption_2ENONE_2E0(A_27a) )
& ( c_2Esptree_2Espt__center_2E1(A_27a,c_2Esptree_2EBN_2E2(A_27a,V2v1_2E0,V1v2_2E0)) = c_2Eoption_2ENONE_2E0(A_27a) ) ) ).
tff(thm_2Esptree_2Espt__center__ind,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)] :
( ( ! [V1x_2E0: A_27a] : p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Esptree_2ELS_2E1(A_27a,V1x_2E0)))
& ! [V2t1_2E0: tyop_2Esptree_2Espt(A_27a),V3x_2E0: A_27a,V4t2_2E0: tyop_2Esptree_2Espt(A_27a)] : p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Esptree_2EBS_2E3(A_27a,V2t1_2E0,V3x_2E0,V4t2_2E0)))
& p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Esptree_2ELN_2E0(A_27a)))
& ! [V5v1_2E0: tyop_2Esptree_2Espt(A_27a),V6v2_2E0: tyop_2Esptree_2Espt(A_27a)] : p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Esptree_2EBN_2E2(A_27a,V5v1_2E0,V6v2_2E0))) )
=> ! [V7v_2E0: tyop_2Esptree_2Espt(A_27a)] : p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V7v_2E0)) ) ).
tff(thm_2Esptree_2Einsert__shadow,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Esptree_2Espt(A_27a),V1a_2E0: tyop_2Enum_2Enum,V2b_2E0: A_27a,V3c_2E0: A_27a] : ( c_2Esptree_2Einsert_2E3(A_27a,V1a_2E0,V2b_2E0,c_2Esptree_2Einsert_2E3(A_27a,V1a_2E0,V3c_2E0,V0t_2E0)) = c_2Esptree_2Einsert_2E3(A_27a,V1a_2E0,V2b_2E0,V0t_2E0) ) ).
tff(thm_2Esptree_2Einsert__insert,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
( ! [V0x1_2E0: tyop_2Enum_2Enum,V1x2_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0x1_2E0),V1x2_2E0))
<=> ( V0x1_2E0 = V1x2_2E0 ) )
=> ! [V0x1_2E0: tyop_2Enum_2Enum,V1x2_2E0: tyop_2Enum_2Enum,V2v1_2E0: A_27a,V3v2_2E0: A_27a,V4t_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Einsert_2E3(A_27a,V0x1_2E0,V2v1_2E0,c_2Esptree_2Einsert_2E3(A_27a,V1x2_2E0,V3v2_2E0,V4t_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V0x1_2E0),V1x2_2E0),c_2Esptree_2Einsert_2E3(A_27a,V0x1_2E0,V2v1_2E0,V4t_2E0),c_2Esptree_2Einsert_2E3(A_27a,V1x2_2E0,V3v2_2E0,c_2Esptree_2Einsert_2E3(A_27a,V0x1_2E0,V2v1_2E0,V4t_2E0))) ) ) ).
tff(thm_2Esptree_2Emap__fromAList,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))] :
( ! [V1f_2E0: tyop_2Emin_2Efun(A_27b,A_27a),V2k_2E0: tyop_2Enum_2Enum,V3v_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),F0_2E0,V1f_2E0),V2k_2E0),V3v_2E0) = c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,A_27a,V2k_2E0,app_2E2(A_27b,A_27a,V1f_2E0,V3v_2E0)) )
=> ! [V0ls_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b)),V1f_2E0: tyop_2Emin_2Efun(A_27b,A_27a)] : ( c_2Esptree_2Emap_2E2(A_27a,A_27b,V1f_2E0,c_2Esptree_2EfromAList_2E1(A_27b,V0ls_2E0)) = c_2Esptree_2EfromAList_2E1(A_27a,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27b),tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2EUNCURRY_2E1(tyop_2Enum_2Enum,A_27b,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),app_2E2(tyop_2Emin_2Efun(A_27b,A_27a),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))),F0_2E0,V1f_2E0)),V0ls_2E0)) ) ) ).
tff(thm_2Esptree_2Emap__insert,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1x_2E0: tyop_2Enum_2Enum,V2y_2E0: A_27a,V3z_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Emap_2E2(A_27b,A_27a,V0f_2E0,c_2Esptree_2Einsert_2E3(A_27a,V1x_2E0,V2y_2E0,V3z_2E0)) = c_2Esptree_2Einsert_2E3(A_27b,V1x_2E0,app_2E2(A_27a,A_27b,V0f_2E0,V2y_2E0),c_2Esptree_2Emap_2E2(A_27b,A_27a,V0f_2E0,V3z_2E0)) ) ).
tff(thm_2Esptree_2Emap__map__o,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0t_2E0: tyop_2Esptree_2Espt(A_27a),V1f_2E0: tyop_2Emin_2Efun(A_27b,A_27c),V2g_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Esptree_2Emap_2E2(A_27c,A_27b,V1f_2E0,c_2Esptree_2Emap_2E2(A_27b,A_27a,V2g_2E0,V0t_2E0)) = c_2Esptree_2Emap_2E2(A_27c,A_27a,c_2Ecombin_2Eo_2E2(A_27a,A_27c,A_27b,V1f_2E0,V2g_2E0),V0t_2E0) ) ).
tff(thm_2Esptree_2Ewf__map,axiom,
! [A_27a: $tType,A_27b: $tType,V0t_2E0: tyop_2Esptree_2Espt(A_27a),V1f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] : ( c_2Esptree_2Ewf_2E1(A_27b,c_2Esptree_2Emap_2E2(A_27b,A_27a,V1f_2E0,V0t_2E0)) = c_2Esptree_2Ewf_2E1(A_27a,V0t_2E0) ) ).
tff(thm_2Esptree_2Emap__LN,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1t_2E0: tyop_2Esptree_2Espt(A_27a)] :
( ( c_2Esptree_2Emap_2E2(A_27b,A_27a,V0f_2E0,V1t_2E0) = c_2Esptree_2ELN_2E0(A_27b) )
<=> ( V1t_2E0 = c_2Esptree_2ELN_2E0(A_27a) ) ) ).
tff(thm_2Esptree_2Elookup__map,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Esptree_2Espt(A_27a),V2x_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Elookup_2E2(A_27b,V2x_2E0,c_2Esptree_2Emap_2E2(A_27b,A_27a,V0f_2E0,V1s_2E0)) = c_2Eoption_2EOPTION__MAP_2E2(A_27a,A_27b,V0f_2E0,c_2Esptree_2Elookup_2E2(A_27a,V2x_2E0,V1s_2E0)) ) ).
tff(thm_2Esptree_2Edomain__map,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Edomain_2E1(A_27b,c_2Esptree_2Emap_2E2(A_27b,A_27a,V0f_2E0,V1s_2E0)) = c_2Esptree_2Edomain_2E1(A_27a,V1s_2E0) ) ).
tff(thm_2Esptree_2EtoList__map,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V1s_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2EtoList_2E1(A_27b,c_2Esptree_2Emap_2E2(A_27b,A_27a,V0f_2E0,V1s_2E0)) = c_2Elist_2EMAP_2E2(A_27a,A_27b,V0f_2E0,c_2Esptree_2EtoList_2E1(A_27a,V1s_2E0)) ) ).
tff(thm_2Esptree_2EfromAList__append,axiom,
! [A_27a: $tType,V0l1_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V1l2_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))] : ( c_2Esptree_2EfromAList_2E1(A_27a,c_2Elist_2EAPPEND_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),V0l1_2E0,V1l2_2E0)) = c_2Esptree_2Eunion_2E2(A_27a,c_2Esptree_2EfromAList_2E1(A_27a,V0l1_2E0),c_2Esptree_2EfromAList_2E1(A_27a,V1l2_2E0)) ) ).
tff(thm_2Esptree_2Eunion__insert__LN,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Enum_2Enum,V1y_2E0: A_27a,V2t2_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Eunion_2E2(A_27a,c_2Esptree_2Einsert_2E3(A_27a,V0x_2E0,V1y_2E0,c_2Esptree_2ELN_2E0(A_27a)),V2t2_2E0) = c_2Esptree_2Einsert_2E3(A_27a,V0x_2E0,V1y_2E0,V2t2_2E0) ) ).
tff(thm_2Esptree_2EfromAList__toAList,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Esptree_2Espt(A_27a)] :
( p(c_2Esptree_2Ewf_2E1(A_27a,V0t_2E0))
=> ( c_2Esptree_2EfromAList_2E1(A_27a,c_2Esptree_2EtoAList_2E1(A_27a,V0t_2E0)) = V0t_2E0 ) ) ).
tff(thm_2Esptree_2Ewf__fromAList,axiom,
! [A_27a: $tType,V0ls_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))] : p(c_2Esptree_2Ewf_2E1(A_27a,c_2Esptree_2EfromAList_2E1(A_27a,V0ls_2E0))) ).
tff(thm_2Esptree_2Elookup__fromAList__toAList,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Esptree_2Espt(A_27a),V1x_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Elookup_2E2(A_27a,V1x_2E0,c_2Esptree_2EfromAList_2E1(A_27a,c_2Esptree_2EtoAList_2E1(A_27a,V0t_2E0))) = c_2Esptree_2Elookup_2E2(A_27a,V1x_2E0,V0t_2E0) ) ).
tff(thm_2Esptree_2Edomain__fromAList,axiom,
! [A_27a: $tType,V0ls_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))] : ( c_2Esptree_2Edomain_2E1(A_27a,c_2Esptree_2EfromAList_2E1(A_27a,V0ls_2E0)) = c_2Elist_2ELIST__TO__SET_2E1(tyop_2Enum_2Enum,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Enum_2Enum,c_2Epair_2EFST_2E0(tyop_2Enum_2Enum,A_27a),V0ls_2E0)) ) ).
tff(thm_2Esptree_2Elookup__fromAList,axiom,
! [A_27a: $tType,V0ls_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V1x_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Elookup_2E2(A_27a,V1x_2E0,c_2Esptree_2EfromAList_2E1(A_27a,V0ls_2E0)) = c_2Ealist_2EALOOKUP_2E2(A_27a,tyop_2Enum_2Enum,V0ls_2E0,V1x_2E0) ) ).
tff(thm_2Esptree_2EfromAList__def,axiom,
! [A_27a: $tType] :
( ( c_2Esptree_2EfromAList_2E1(A_27a,c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))) = c_2Esptree_2ELN_2E0(A_27a) )
& ! [V0y_2E0: A_27a,V1xs_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),V2x_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2EfromAList_2E1(A_27a,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,A_27a,V2x_2E0,V0y_2E0),V1xs_2E0)) = c_2Esptree_2Einsert_2E3(A_27a,V2x_2E0,V0y_2E0,c_2Esptree_2EfromAList_2E1(A_27a,V1xs_2E0)) ) ) ).
tff(thm_2Esptree_2EfromAList__ind,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool)] :
( ( p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2ENIL_2E0(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))))
& ! [V1x_2E0: tyop_2Enum_2Enum,V2y_2E0: A_27a,V3xs_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))] :
( p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool,V0P_2E0,V3xs_2E0))
=> p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool,V0P_2E0,c_2Elist_2ECONS_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,A_27a,V1x_2E0,V2y_2E0),V3xs_2E0))) ) )
=> ! [V4v_2E0: tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a))] : p(app_2E2(tyop_2Elist_2Elist(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a)),tyop_2Emin_2Ebool,V0P_2E0,V4v_2E0)) ) ).
tff(thm_2Esptree_2Edelete__compute,axiom,
! [A_27a: $tType,V0t2_2E0: tyop_2Esptree_2Espt(A_27a),V1t1_2E0: tyop_2Esptree_2Espt(A_27a),V2t_2E0: tyop_2Esptree_2Espt(A_27a),V3n_2E0: tyop_2Enum_2Enum,V4a_2E0: A_27a] :
( ( c_2Esptree_2Edelete_2E2(A_27a,c_2Earithmetic_2ENUMERAL_2E1(V3n_2E0),V2t_2E0) = c_2Esptree_2Edelete_2E2(A_27a,V3n_2E0,V2t_2E0) )
& ( c_2Esptree_2Edelete_2E2(A_27a,c_2Enum_2E0_2E0,c_2Esptree_2ELN_2E0(A_27a)) = c_2Esptree_2ELN_2E0(A_27a) )
& ( c_2Esptree_2Edelete_2E2(A_27a,c_2Enum_2E0_2E0,c_2Esptree_2ELS_2E1(A_27a,V4a_2E0)) = c_2Esptree_2ELN_2E0(A_27a) )
& ( c_2Esptree_2Edelete_2E2(A_27a,c_2Enum_2E0_2E0,c_2Esptree_2EBN_2E2(A_27a,V1t1_2E0,V0t2_2E0)) = c_2Esptree_2EBN_2E2(A_27a,V1t1_2E0,V0t2_2E0) )
& ( c_2Esptree_2Edelete_2E2(A_27a,c_2Enum_2E0_2E0,c_2Esptree_2EBS_2E3(A_27a,V1t1_2E0,V4a_2E0,V0t2_2E0)) = c_2Esptree_2EBN_2E2(A_27a,V1t1_2E0,V0t2_2E0) )
& ( c_2Esptree_2Edelete_2E2(A_27a,c_2Earithmetic_2EZERO_2E0,c_2Esptree_2ELN_2E0(A_27a)) = c_2Esptree_2ELN_2E0(A_27a) )
& ( c_2Esptree_2Edelete_2E2(A_27a,c_2Earithmetic_2EZERO_2E0,c_2Esptree_2ELS_2E1(A_27a,V4a_2E0)) = c_2Esptree_2ELN_2E0(A_27a) )
& ( c_2Esptree_2Edelete_2E2(A_27a,c_2Earithmetic_2EZERO_2E0,c_2Esptree_2EBN_2E2(A_27a,V1t1_2E0,V0t2_2E0)) = c_2Esptree_2EBN_2E2(A_27a,V1t1_2E0,V0t2_2E0) )
& ( c_2Esptree_2Edelete_2E2(A_27a,c_2Earithmetic_2EZERO_2E0,c_2Esptree_2EBS_2E3(A_27a,V1t1_2E0,V4a_2E0,V0t2_2E0)) = c_2Esptree_2EBN_2E2(A_27a,V1t1_2E0,V0t2_2E0) )
& ( c_2Esptree_2Edelete_2E2(A_27a,c_2Earithmetic_2EBIT1_2E1(V3n_2E0),c_2Esptree_2ELN_2E0(A_27a)) = c_2Esptree_2ELN_2E0(A_27a) )
& ( c_2Esptree_2Edelete_2E2(A_27a,c_2Earithmetic_2EBIT1_2E1(V3n_2E0),c_2Esptree_2ELS_2E1(A_27a,V4a_2E0)) = c_2Esptree_2ELS_2E1(A_27a,V4a_2E0) )
& ( c_2Esptree_2Edelete_2E2(A_27a,c_2Earithmetic_2EBIT1_2E1(V3n_2E0),c_2Esptree_2EBN_2E2(A_27a,V1t1_2E0,V0t2_2E0)) = c_2Esptree_2Emk__BN_2E2(A_27a,V1t1_2E0,c_2Esptree_2Edelete_2E2(A_27a,V3n_2E0,V0t2_2E0)) )
& ( c_2Esptree_2Edelete_2E2(A_27a,c_2Earithmetic_2EBIT1_2E1(V3n_2E0),c_2Esptree_2EBS_2E3(A_27a,V1t1_2E0,V4a_2E0,V0t2_2E0)) = c_2Esptree_2Emk__BS_2E3(A_27a,V1t1_2E0,V4a_2E0,c_2Esptree_2Edelete_2E2(A_27a,V3n_2E0,V0t2_2E0)) )
& ( c_2Esptree_2Edelete_2E2(A_27a,c_2Earithmetic_2EBIT2_2E1(V3n_2E0),c_2Esptree_2ELN_2E0(A_27a)) = c_2Esptree_2ELN_2E0(A_27a) )
& ( c_2Esptree_2Edelete_2E2(A_27a,c_2Earithmetic_2EBIT2_2E1(V3n_2E0),c_2Esptree_2ELS_2E1(A_27a,V4a_2E0)) = c_2Esptree_2ELS_2E1(A_27a,V4a_2E0) )
& ( c_2Esptree_2Edelete_2E2(A_27a,c_2Earithmetic_2EBIT2_2E1(V3n_2E0),c_2Esptree_2EBN_2E2(A_27a,V1t1_2E0,V0t2_2E0)) = c_2Esptree_2Emk__BN_2E2(A_27a,c_2Esptree_2Edelete_2E2(A_27a,V3n_2E0,V1t1_2E0),V0t2_2E0) )
& ( c_2Esptree_2Edelete_2E2(A_27a,c_2Earithmetic_2EBIT2_2E1(V3n_2E0),c_2Esptree_2EBS_2E3(A_27a,V1t1_2E0,V4a_2E0,V0t2_2E0)) = c_2Esptree_2Emk__BS_2E3(A_27a,c_2Esptree_2Edelete_2E2(A_27a,V3n_2E0,V1t1_2E0),V4a_2E0,V0t2_2E0) ) ) ).
tff(thm_2Esptree_2Einsert__compute,axiom,
! [A_27a: $tType,V0t2_2E0: tyop_2Esptree_2Espt(A_27a),V1t1_2E0: tyop_2Esptree_2Espt(A_27a),V2t_2E0: tyop_2Esptree_2Espt(A_27a),V3n_2E0: tyop_2Enum_2Enum,V4a_27_2E0: A_27a,V5a_2E0: A_27a] :
( ( c_2Esptree_2Einsert_2E3(A_27a,c_2Earithmetic_2ENUMERAL_2E1(V3n_2E0),V5a_2E0,V2t_2E0) = c_2Esptree_2Einsert_2E3(A_27a,V3n_2E0,V5a_2E0,V2t_2E0) )
& ( c_2Esptree_2Einsert_2E3(A_27a,c_2Enum_2E0_2E0,V5a_2E0,c_2Esptree_2ELN_2E0(A_27a)) = c_2Esptree_2ELS_2E1(A_27a,V5a_2E0) )
& ( c_2Esptree_2Einsert_2E3(A_27a,c_2Enum_2E0_2E0,V5a_2E0,c_2Esptree_2ELS_2E1(A_27a,V4a_27_2E0)) = c_2Esptree_2ELS_2E1(A_27a,V5a_2E0) )
& ( c_2Esptree_2Einsert_2E3(A_27a,c_2Enum_2E0_2E0,V5a_2E0,c_2Esptree_2EBN_2E2(A_27a,V1t1_2E0,V0t2_2E0)) = c_2Esptree_2EBS_2E3(A_27a,V1t1_2E0,V5a_2E0,V0t2_2E0) )
& ( c_2Esptree_2Einsert_2E3(A_27a,c_2Enum_2E0_2E0,V5a_2E0,c_2Esptree_2EBS_2E3(A_27a,V1t1_2E0,V4a_27_2E0,V0t2_2E0)) = c_2Esptree_2EBS_2E3(A_27a,V1t1_2E0,V5a_2E0,V0t2_2E0) )
& ( c_2Esptree_2Einsert_2E3(A_27a,c_2Earithmetic_2EZERO_2E0,V5a_2E0,c_2Esptree_2ELN_2E0(A_27a)) = c_2Esptree_2ELS_2E1(A_27a,V5a_2E0) )
& ( c_2Esptree_2Einsert_2E3(A_27a,c_2Earithmetic_2EZERO_2E0,V5a_2E0,c_2Esptree_2ELS_2E1(A_27a,V4a_27_2E0)) = c_2Esptree_2ELS_2E1(A_27a,V5a_2E0) )
& ( c_2Esptree_2Einsert_2E3(A_27a,c_2Earithmetic_2EZERO_2E0,V5a_2E0,c_2Esptree_2EBN_2E2(A_27a,V1t1_2E0,V0t2_2E0)) = c_2Esptree_2EBS_2E3(A_27a,V1t1_2E0,V5a_2E0,V0t2_2E0) )
& ( c_2Esptree_2Einsert_2E3(A_27a,c_2Earithmetic_2EZERO_2E0,V5a_2E0,c_2Esptree_2EBS_2E3(A_27a,V1t1_2E0,V4a_27_2E0,V0t2_2E0)) = c_2Esptree_2EBS_2E3(A_27a,V1t1_2E0,V5a_2E0,V0t2_2E0) )
& ( c_2Esptree_2Einsert_2E3(A_27a,c_2Earithmetic_2EBIT1_2E1(V3n_2E0),V5a_2E0,c_2Esptree_2ELN_2E0(A_27a)) = c_2Esptree_2EBN_2E2(A_27a,c_2Esptree_2ELN_2E0(A_27a),c_2Esptree_2Einsert_2E3(A_27a,V3n_2E0,V5a_2E0,c_2Esptree_2ELN_2E0(A_27a))) )
& ( c_2Esptree_2Einsert_2E3(A_27a,c_2Earithmetic_2EBIT1_2E1(V3n_2E0),V5a_2E0,c_2Esptree_2ELS_2E1(A_27a,V4a_27_2E0)) = c_2Esptree_2EBS_2E3(A_27a,c_2Esptree_2ELN_2E0(A_27a),V4a_27_2E0,c_2Esptree_2Einsert_2E3(A_27a,V3n_2E0,V5a_2E0,c_2Esptree_2ELN_2E0(A_27a))) )
& ( c_2Esptree_2Einsert_2E3(A_27a,c_2Earithmetic_2EBIT1_2E1(V3n_2E0),V5a_2E0,c_2Esptree_2EBN_2E2(A_27a,V1t1_2E0,V0t2_2E0)) = c_2Esptree_2EBN_2E2(A_27a,V1t1_2E0,c_2Esptree_2Einsert_2E3(A_27a,V3n_2E0,V5a_2E0,V0t2_2E0)) )
& ( c_2Esptree_2Einsert_2E3(A_27a,c_2Earithmetic_2EBIT1_2E1(V3n_2E0),V5a_2E0,c_2Esptree_2EBS_2E3(A_27a,V1t1_2E0,V4a_27_2E0,V0t2_2E0)) = c_2Esptree_2EBS_2E3(A_27a,V1t1_2E0,V4a_27_2E0,c_2Esptree_2Einsert_2E3(A_27a,V3n_2E0,V5a_2E0,V0t2_2E0)) )
& ( c_2Esptree_2Einsert_2E3(A_27a,c_2Earithmetic_2EBIT2_2E1(V3n_2E0),V5a_2E0,c_2Esptree_2ELN_2E0(A_27a)) = c_2Esptree_2EBN_2E2(A_27a,c_2Esptree_2Einsert_2E3(A_27a,V3n_2E0,V5a_2E0,c_2Esptree_2ELN_2E0(A_27a)),c_2Esptree_2ELN_2E0(A_27a)) )
& ( c_2Esptree_2Einsert_2E3(A_27a,c_2Earithmetic_2EBIT2_2E1(V3n_2E0),V5a_2E0,c_2Esptree_2ELS_2E1(A_27a,V4a_27_2E0)) = c_2Esptree_2EBS_2E3(A_27a,c_2Esptree_2Einsert_2E3(A_27a,V3n_2E0,V5a_2E0,c_2Esptree_2ELN_2E0(A_27a)),V4a_27_2E0,c_2Esptree_2ELN_2E0(A_27a)) )
& ( c_2Esptree_2Einsert_2E3(A_27a,c_2Earithmetic_2EBIT2_2E1(V3n_2E0),V5a_2E0,c_2Esptree_2EBN_2E2(A_27a,V1t1_2E0,V0t2_2E0)) = c_2Esptree_2EBN_2E2(A_27a,c_2Esptree_2Einsert_2E3(A_27a,V3n_2E0,V5a_2E0,V1t1_2E0),V0t2_2E0) )
& ( c_2Esptree_2Einsert_2E3(A_27a,c_2Earithmetic_2EBIT2_2E1(V3n_2E0),V5a_2E0,c_2Esptree_2EBS_2E3(A_27a,V1t1_2E0,V4a_27_2E0,V0t2_2E0)) = c_2Esptree_2EBS_2E3(A_27a,c_2Esptree_2Einsert_2E3(A_27a,V3n_2E0,V5a_2E0,V1t1_2E0),V4a_27_2E0,V0t2_2E0) ) ) ).
tff(thm_2Esptree_2Elookup__compute,axiom,
! [A_27a: $tType,V0t2_2E0: tyop_2Esptree_2Espt(A_27a),V1t1_2E0: tyop_2Esptree_2Espt(A_27a),V2t_2E0: tyop_2Esptree_2Espt(A_27a),V3n_2E0: tyop_2Enum_2Enum,V4a_2E0: A_27a] :
( ( c_2Esptree_2Elookup_2E2(A_27a,c_2Earithmetic_2ENUMERAL_2E1(V3n_2E0),V2t_2E0) = c_2Esptree_2Elookup_2E2(A_27a,V3n_2E0,V2t_2E0) )
& ( c_2Esptree_2Elookup_2E2(A_27a,c_2Enum_2E0_2E0,c_2Esptree_2ELN_2E0(A_27a)) = c_2Eoption_2ENONE_2E0(A_27a) )
& ( c_2Esptree_2Elookup_2E2(A_27a,c_2Enum_2E0_2E0,c_2Esptree_2ELS_2E1(A_27a,V4a_2E0)) = c_2Eoption_2ESOME_2E1(A_27a,V4a_2E0) )
& ( c_2Esptree_2Elookup_2E2(A_27a,c_2Enum_2E0_2E0,c_2Esptree_2EBN_2E2(A_27a,V1t1_2E0,V0t2_2E0)) = c_2Eoption_2ENONE_2E0(A_27a) )
& ( c_2Esptree_2Elookup_2E2(A_27a,c_2Enum_2E0_2E0,c_2Esptree_2EBS_2E3(A_27a,V1t1_2E0,V4a_2E0,V0t2_2E0)) = c_2Eoption_2ESOME_2E1(A_27a,V4a_2E0) )
& ( c_2Esptree_2Elookup_2E2(A_27a,c_2Earithmetic_2EZERO_2E0,c_2Esptree_2ELN_2E0(A_27a)) = c_2Eoption_2ENONE_2E0(A_27a) )
& ( c_2Esptree_2Elookup_2E2(A_27a,c_2Earithmetic_2EZERO_2E0,c_2Esptree_2ELS_2E1(A_27a,V4a_2E0)) = c_2Eoption_2ESOME_2E1(A_27a,V4a_2E0) )
& ( c_2Esptree_2Elookup_2E2(A_27a,c_2Earithmetic_2EZERO_2E0,c_2Esptree_2EBN_2E2(A_27a,V1t1_2E0,V0t2_2E0)) = c_2Eoption_2ENONE_2E0(A_27a) )
& ( c_2Esptree_2Elookup_2E2(A_27a,c_2Earithmetic_2EZERO_2E0,c_2Esptree_2EBS_2E3(A_27a,V1t1_2E0,V4a_2E0,V0t2_2E0)) = c_2Eoption_2ESOME_2E1(A_27a,V4a_2E0) )
& ( c_2Esptree_2Elookup_2E2(A_27a,c_2Earithmetic_2EBIT1_2E1(V3n_2E0),c_2Esptree_2ELN_2E0(A_27a)) = c_2Eoption_2ENONE_2E0(A_27a) )
& ( c_2Esptree_2Elookup_2E2(A_27a,c_2Earithmetic_2EBIT1_2E1(V3n_2E0),c_2Esptree_2ELS_2E1(A_27a,V4a_2E0)) = c_2Eoption_2ENONE_2E0(A_27a) )
& ( c_2Esptree_2Elookup_2E2(A_27a,c_2Earithmetic_2EBIT1_2E1(V3n_2E0),c_2Esptree_2EBN_2E2(A_27a,V1t1_2E0,V0t2_2E0)) = c_2Esptree_2Elookup_2E2(A_27a,V3n_2E0,V0t2_2E0) )
& ( c_2Esptree_2Elookup_2E2(A_27a,c_2Earithmetic_2EBIT1_2E1(V3n_2E0),c_2Esptree_2EBS_2E3(A_27a,V1t1_2E0,V4a_2E0,V0t2_2E0)) = c_2Esptree_2Elookup_2E2(A_27a,V3n_2E0,V0t2_2E0) )
& ( c_2Esptree_2Elookup_2E2(A_27a,c_2Earithmetic_2EBIT2_2E1(V3n_2E0),c_2Esptree_2ELN_2E0(A_27a)) = c_2Eoption_2ENONE_2E0(A_27a) )
& ( c_2Esptree_2Elookup_2E2(A_27a,c_2Earithmetic_2EBIT2_2E1(V3n_2E0),c_2Esptree_2ELS_2E1(A_27a,V4a_2E0)) = c_2Eoption_2ENONE_2E0(A_27a) )
& ( c_2Esptree_2Elookup_2E2(A_27a,c_2Earithmetic_2EBIT2_2E1(V3n_2E0),c_2Esptree_2EBN_2E2(A_27a,V1t1_2E0,V0t2_2E0)) = c_2Esptree_2Elookup_2E2(A_27a,V3n_2E0,V1t1_2E0) )
& ( c_2Esptree_2Elookup_2E2(A_27a,c_2Earithmetic_2EBIT2_2E1(V3n_2E0),c_2Esptree_2EBS_2E3(A_27a,V1t1_2E0,V4a_2E0,V0t2_2E0)) = c_2Esptree_2Elookup_2E2(A_27a,V3n_2E0,V1t1_2E0) ) ) ).
tff(thm_2Esptree_2Einter__assoc,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0t1_2E0: tyop_2Esptree_2Espt(A_27a),V1t2_2E0: tyop_2Esptree_2Espt(A_27b),V2t3_2E0: tyop_2Esptree_2Espt(A_27c)] : ( c_2Esptree_2Einter_2E2(A_27a,A_27b,V0t1_2E0,c_2Esptree_2Einter_2E2(A_27b,A_27c,V1t2_2E0,V2t3_2E0)) = c_2Esptree_2Einter_2E2(A_27a,A_27c,c_2Esptree_2Einter_2E2(A_27a,A_27b,V0t1_2E0,V1t2_2E0),V2t3_2E0) ) ).
tff(thm_2Esptree_2Eunion__assoc,axiom,
! [A_27a: $tType,V0t1_2E0: tyop_2Esptree_2Espt(A_27a),V1t2_2E0: tyop_2Esptree_2Espt(A_27a),V2t3_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Eunion_2E2(A_27a,V0t1_2E0,c_2Esptree_2Eunion_2E2(A_27a,V1t2_2E0,V2t3_2E0)) = c_2Esptree_2Eunion_2E2(A_27a,c_2Esptree_2Eunion_2E2(A_27a,V0t1_2E0,V1t2_2E0),V2t3_2E0) ) ).
tff(thm_2Esptree_2Einter__LN,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0t_2E0: tyop_2Esptree_2Espt(A_27a)] :
( ( c_2Esptree_2Einter_2E2(A_27a,A_27b,V0t_2E0,c_2Esptree_2ELN_2E0(A_27b)) = c_2Esptree_2ELN_2E0(A_27a) )
& ( c_2Esptree_2Einter_2E2(A_27c,A_27a,c_2Esptree_2ELN_2E0(A_27c),V0t_2E0) = c_2Esptree_2ELN_2E0(A_27c) ) ) ).
tff(thm_2Esptree_2Eunion__LN,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Esptree_2Espt(A_27a)] :
( ( c_2Esptree_2Eunion_2E2(A_27a,V0t_2E0,c_2Esptree_2ELN_2E0(A_27a)) = V0t_2E0 )
& ( c_2Esptree_2Eunion_2E2(A_27a,c_2Esptree_2ELN_2E0(A_27a),V0t_2E0) = V0t_2E0 ) ) ).
tff(thm_2Esptree_2Edelete__mk__wf,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Enum_2Enum,V1t_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Edelete_2E2(A_27a,V0x_2E0,c_2Esptree_2Emk__wf_2E1(A_27a,V1t_2E0)) = c_2Esptree_2Emk__wf_2E1(A_27a,c_2Esptree_2Edelete_2E2(A_27a,V0x_2E0,V1t_2E0)) ) ).
tff(thm_2Esptree_2Einsert__mk__wf,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Enum_2Enum,V1v_2E0: A_27a,V2t_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Einsert_2E3(A_27a,V0x_2E0,V1v_2E0,c_2Esptree_2Emk__wf_2E1(A_27a,V2t_2E0)) = c_2Esptree_2Emk__wf_2E1(A_27a,c_2Esptree_2Einsert_2E3(A_27a,V0x_2E0,V1v_2E0,V2t_2E0)) ) ).
tff(thm_2Esptree_2Einter__mk__wf,axiom,
! [A_27a: $tType,A_27b: $tType,V0t1_2E0: tyop_2Esptree_2Espt(A_27a),V1t2_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Einter_2E2(A_27a,A_27b,c_2Esptree_2Emk__wf_2E1(A_27a,V0t1_2E0),c_2Esptree_2Emk__wf_2E1(A_27b,V1t2_2E0)) = c_2Esptree_2Emk__wf_2E1(A_27a,c_2Esptree_2Einter_2E2(A_27a,A_27b,V0t1_2E0,V1t2_2E0)) ) ).
tff(thm_2Esptree_2Eunion__mk__wf,axiom,
! [A_27a: $tType,V0t1_2E0: tyop_2Esptree_2Espt(A_27a),V1t2_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Eunion_2E2(A_27a,c_2Esptree_2Emk__wf_2E1(A_27a,V0t1_2E0),c_2Esptree_2Emk__wf_2E1(A_27a,V1t2_2E0)) = c_2Esptree_2Emk__wf_2E1(A_27a,c_2Esptree_2Eunion_2E2(A_27a,V0t1_2E0,V1t2_2E0)) ) ).
tff(thm_2Esptree_2Einter__eq,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0t1_2E0: tyop_2Esptree_2Espt(A_27a),V1t2_2E0: tyop_2Esptree_2Espt(A_27b),V2t3_2E0: tyop_2Esptree_2Espt(A_27a),V3t4_2E0: tyop_2Esptree_2Espt(A_27c)] :
( ( c_2Esptree_2Einter_2E2(A_27a,A_27b,V0t1_2E0,V1t2_2E0) = c_2Esptree_2Einter_2E2(A_27a,A_27c,V2t3_2E0,V3t4_2E0) )
<=> ! [V4x_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Elookup_2E2(A_27a,V4x_2E0,c_2Esptree_2Einter_2E2(A_27a,A_27b,V0t1_2E0,V1t2_2E0)) = c_2Esptree_2Elookup_2E2(A_27a,V4x_2E0,c_2Esptree_2Einter_2E2(A_27a,A_27c,V2t3_2E0,V3t4_2E0)) ) ) ).
tff(thm_2Esptree_2Emk__wf__eq,axiom,
! [A_27a: $tType,V0t1_2E0: tyop_2Esptree_2Espt(A_27a),V1t2_2E0: tyop_2Esptree_2Espt(A_27a)] :
( ( c_2Esptree_2Emk__wf_2E1(A_27a,V0t1_2E0) = c_2Esptree_2Emk__wf_2E1(A_27a,V1t2_2E0) )
<=> ! [V2x_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Elookup_2E2(A_27a,V2x_2E0,V0t1_2E0) = c_2Esptree_2Elookup_2E2(A_27a,V2x_2E0,V1t2_2E0) ) ) ).
tff(thm_2Esptree_2Edomain__mk__wf,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Edomain_2E1(A_27a,c_2Esptree_2Emk__wf_2E1(A_27a,V0t_2E0)) = c_2Esptree_2Edomain_2E1(A_27a,V0t_2E0) ) ).
tff(thm_2Esptree_2Elookup__mk__wf,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Enum_2Enum,V1t_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Elookup_2E2(A_27a,V0x_2E0,c_2Esptree_2Emk__wf_2E1(A_27a,V1t_2E0)) = c_2Esptree_2Elookup_2E2(A_27a,V0x_2E0,V1t_2E0) ) ).
tff(thm_2Esptree_2Ewf__mk__id,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Esptree_2Espt(A_27a)] :
( p(c_2Esptree_2Ewf_2E1(A_27a,V0t_2E0))
=> ( c_2Esptree_2Emk__wf_2E1(A_27a,V0t_2E0) = V0t_2E0 ) ) ).
tff(thm_2Esptree_2Ewf__mk__wf,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Esptree_2Espt(A_27a)] : p(c_2Esptree_2Ewf_2E1(A_27a,c_2Esptree_2Emk__wf_2E1(A_27a,V0t_2E0))) ).
tff(thm_2Esptree_2Espt__eq__thm,axiom,
! [A_27a: $tType,V0t1_2E0: tyop_2Esptree_2Espt(A_27a),V1t2_2E0: tyop_2Esptree_2Espt(A_27a)] :
( ( p(c_2Esptree_2Ewf_2E1(A_27a,V0t1_2E0))
& p(c_2Esptree_2Ewf_2E1(A_27a,V1t2_2E0)) )
=> ( ( V0t1_2E0 = V1t2_2E0 )
<=> ! [V2n_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Elookup_2E2(A_27a,V2n_2E0,V0t1_2E0) = c_2Esptree_2Elookup_2E2(A_27a,V2n_2E0,V1t2_2E0) ) ) ) ).
tff(thm_2Esptree_2EMEM__toList,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1t_2E0: tyop_2Esptree_2Espt(A_27a)] :
( p(c_2Ebool_2EIN_2E2(A_27a,V0x_2E0,c_2Elist_2ELIST__TO__SET_2E1(A_27a,c_2Esptree_2EtoList_2E1(A_27a,V1t_2E0))))
<=> ? [V2k_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Elookup_2E2(A_27a,V2k_2E0,V1t_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V0x_2E0) ) ) ).
tff(thm_2Esptree_2EisEmpty__toList,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Esptree_2Espt(A_27a)] :
( p(c_2Esptree_2Ewf_2E1(A_27a,V0t_2E0))
=> ( ( V0t_2E0 = c_2Esptree_2ELN_2E0(A_27a) )
<=> ( c_2Esptree_2EtoList_2E1(A_27a,V0t_2E0) = c_2Elist_2ENIL_2E0(A_27a) ) ) ) ).
tff(thm_2Esptree_2EisEmpty__toListA,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Esptree_2Espt(A_27a),V1acc_2E0: tyop_2Elist_2Elist(A_27a)] :
( p(c_2Esptree_2Ewf_2E1(A_27a,V0t_2E0))
=> ( ( V0t_2E0 = c_2Esptree_2ELN_2E0(A_27a) )
<=> ( c_2Esptree_2EtoListA_2E2(A_27a,V1acc_2E0,V0t_2E0) = V1acc_2E0 ) ) ) ).
tff(thm_2Esptree_2EtoListA__append,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Esptree_2Espt(A_27a),V1acc_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Esptree_2EtoListA_2E2(A_27a,V1acc_2E0,V0t_2E0) = c_2Elist_2EAPPEND_2E2(A_27a,c_2Esptree_2EtoListA_2E2(A_27a,c_2Elist_2ENIL_2E0(A_27a),V0t_2E0),V1acc_2E0) ) ).
tff(thm_2Esptree_2Efoldi__FOLDR__toAList,axiom,
! [A_27a: $tType,A_27b: $tType,V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,A_27b))),V1a_2E0: A_27b,V2t_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Efoldi_2E4(A_27b,A_27a,V0f_2E0,c_2Enum_2E0_2E0,V1a_2E0,V2t_2E0) = c_2Elist_2EFOLDR_2E3(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),A_27b,c_2Epair_2EUNCURRY_2E1(tyop_2Enum_2Enum,A_27a,tyop_2Emin_2Efun(A_27b,A_27b),V0f_2E0),V1a_2E0,c_2Esptree_2EtoAList_2E1(A_27a,V2t_2E0)) ) ).
tff(thm_2Esptree_2EALL__DISTINCT__MAP__FST__toAList,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Esptree_2Espt(A_27a)] : p(c_2Elist_2EALL__DISTINCT_2E1(tyop_2Enum_2Enum,c_2Elist_2EMAP_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),tyop_2Enum_2Enum,c_2Epair_2EFST_2E0(tyop_2Enum_2Enum,A_27a),c_2Esptree_2EtoAList_2E1(A_27a,V0t_2E0)))) ).
tff(thm_2Esptree_2Edomain__empty,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Esptree_2Espt(A_27a)] :
( p(c_2Esptree_2Ewf_2E1(A_27a,V0t_2E0))
=> ( ( V0t_2E0 = c_2Esptree_2ELN_2E0(A_27a) )
<=> ( c_2Esptree_2Edomain_2E1(A_27a,V0t_2E0) = c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum) ) ) ) ).
tff(thm_2Esptree_2Einsert__union,axiom,
! [A_27a: $tType,V0k_2E0: tyop_2Enum_2Enum,V1v_2E0: A_27a,V2s_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Einsert_2E3(A_27a,V0k_2E0,V1v_2E0,V2s_2E0) = c_2Esptree_2Eunion_2E2(A_27a,c_2Esptree_2Einsert_2E3(A_27a,V0k_2E0,V1v_2E0,c_2Esptree_2ELN_2E0(A_27a)),V2s_2E0) ) ).
tff(thm_2Esptree_2EALOOKUP__toAList,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Esptree_2Espt(A_27a),V1x_2E0: tyop_2Enum_2Enum] : ( c_2Ealist_2EALOOKUP_2E2(A_27a,tyop_2Enum_2Enum,c_2Esptree_2EtoAList_2E1(A_27a,V0t_2E0),V1x_2E0) = c_2Esptree_2Elookup_2E2(A_27a,V1x_2E0,V0t_2E0) ) ).
tff(thm_2Esptree_2EMEM__toAList,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Esptree_2Espt(A_27a),V1k_2E0: tyop_2Enum_2Enum,V2v_2E0: A_27a] :
( p(c_2Ebool_2EIN_2E2(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Epair_2E_2C_2E2(tyop_2Enum_2Enum,A_27a,V1k_2E0,V2v_2E0),c_2Elist_2ELIST__TO__SET_2E1(tyop_2Epair_2Eprod(tyop_2Enum_2Enum,A_27a),c_2Esptree_2EtoAList_2E1(A_27a,V0t_2E0))))
<=> ( c_2Esptree_2Elookup_2E2(A_27a,V1k_2E0,V0t_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V2v_2E0) ) ) ).
tff(thm_2Esptree_2Elookup__mapi,axiom,
! [A_27a: $tType,A_27b: $tType,V0pt_2E0: tyop_2Esptree_2Espt(A_27b),V1k_2E0: tyop_2Enum_2Enum,V2f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a))] : ( c_2Esptree_2Elookup_2E2(A_27a,V1k_2E0,c_2Esptree_2Emapi_2E2(A_27a,A_27b,V2f_2E0,V0pt_2E0)) = c_2Eoption_2EOPTION__MAP_2E2(A_27b,A_27a,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27b,A_27a),V2f_2E0,V1k_2E0),c_2Esptree_2Elookup_2E2(A_27b,V1k_2E0,V0pt_2E0)) ) ).
tff(thm_2Esptree_2Elookup__mapi0,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))))] :
( ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),V2i_2E0: tyop_2Enum_2Enum,V3k_2E0: tyop_2Enum_2Enum,V4v_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27b),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))),F0_2E0,V0f_2E0),V2i_2E0),V3k_2E0),V4v_2E0) = c_2Eoption_2ESOME_2E1(A_27b,app_2E2(A_27a,A_27b,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b),V0f_2E0,c_2Esptree_2Espt__acc_2E2(V2i_2E0,V3k_2E0)),V4v_2E0)) )
=> ! [V0f_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),V1pt_2E0: tyop_2Esptree_2Espt(A_27a),V2i_2E0: tyop_2Enum_2Enum,V3k_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Elookup_2E2(A_27b,V3k_2E0,c_2Esptree_2Emapi0_2E3(A_27b,A_27a,V0f_2E0,V2i_2E0,V1pt_2E0)) = c_2Eoption_2Eoption__CASE_2E3(A_27a,tyop_2Eoption_2Eoption(A_27b),c_2Esptree_2Elookup_2E2(A_27a,V3k_2E0,V1pt_2E0),c_2Eoption_2ENONE_2E0(A_27b),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b))),app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,A_27b)),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27b)))),F0_2E0,V0f_2E0),V2i_2E0),V3k_2E0)) ) ) ).
tff(thm_2Esptree_2Edomain__foldi,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))))] :
( ! [V1k_2E0: tyop_2Enum_2Enum,V2v_2E0: A_27a,V3a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F0_2E0,V1k_2E0),V2v_2E0),V3a_2E0) = c_2Epred__set_2EINSERT_2E2(tyop_2Enum_2Enum,V1k_2E0,V3a_2E0) )
=> ! [V0t_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Edomain_2E1(A_27a,V0t_2E0) = c_2Esptree_2Efoldi_2E4(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),A_27a,F0_2E0,c_2Enum_2E0_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum),V0t_2E0) ) ) ).
tff(thm_2Esptree_2Eset__foldi__keys,axiom,
! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum)),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))))] :
( ! [V2i_2E0: tyop_2Enum_2Enum,V6n_2E0: tyop_2Enum_2Enum] : ( app_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),F1_2E0,V2i_2E0),V6n_2E0) = c_2Earithmetic_2E_2B_2E2(V2i_2E0,c_2Earithmetic_2E_2A_2E2(c_2Esptree_2Elrnext_2E1(V2i_2E0),V6n_2E0)) )
=> ( ! [V3k_2E0: tyop_2Enum_2Enum,V4v_2E0: A_27a,V5a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] : ( app_2E2(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))),F0_2E0,V3k_2E0),V4v_2E0),V5a_2E0) = c_2Epred__set_2EINSERT_2E2(tyop_2Enum_2Enum,V3k_2E0,V5a_2E0) )
=> ! [V0t_2E0: tyop_2Esptree_2Espt(A_27a),V1a_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V2i_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Efoldi_2E4(tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),A_27a,F0_2E0,V2i_2E0,V1a_2E0,V0t_2E0) = c_2Epred__set_2EUNION_2E2(tyop_2Enum_2Enum,V1a_2E0,c_2Epred__set_2EIMAGE_2E2(tyop_2Enum_2Enum,tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Enum_2Enum),F1_2E0,V2i_2E0),c_2Esptree_2Edomain_2E1(A_27a,V0t_2E0))) ) ) ) ).
tff(thm_2Esptree_2Espt__acc__0,axiom,
! [V0k_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Espt__acc_2E2(c_2Enum_2E0_2E0,V0k_2E0) = V0k_2E0 ) ).
tff(thm_2Esptree_2Espt__acc__eqn,axiom,
! [V0k_2E0: tyop_2Enum_2Enum,V1i_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Espt__acc_2E2(V1i_2E0,V0k_2E0) = c_2Earithmetic_2E_2B_2E2(c_2Earithmetic_2E_2A_2E2(c_2Esptree_2Elrnext_2E1(V1i_2E0),V0k_2E0),V1i_2E0) ) ).
tff(thm_2Esptree_2Espt__acc__thm,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( ! [V0k_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V0k_2E0))
<=> ( V0k_2E0 = c_2Enum_2E0_2E0 ) )
=> ! [V0k_2E0: tyop_2Enum_2Enum,V1i_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Espt__acc_2E2(V1i_2E0,V0k_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V0k_2E0),V1i_2E0,c_2Esptree_2Espt__acc_2E2(c_2Earithmetic_2E_2B_2E2(V1i_2E0,c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Earithmetic_2EEVEN_2E1(V0k_2E0),c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Esptree_2Elrnext_2E1(V1i_2E0)),c_2Esptree_2Elrnext_2E1(V1i_2E0))),c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V0k_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))) ) ) ).
tff(thm_2Esptree_2Espt__acc__def__compute,axiom,
( ! [V0i_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Espt__acc_2E2(V0i_2E0,c_2Enum_2E0_2E0) = V0i_2E0 )
& ! [V1k_2E0: tyop_2Enum_2Enum,V2i_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Espt__acc_2E2(V2i_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1k_2E0))) = c_2Esptree_2Espt__acc_2E2(c_2Earithmetic_2E_2B_2E2(V2i_2E0,c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Earithmetic_2EEVEN_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1k_2E0))),c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Esptree_2Elrnext_2E1(V2i_2E0)),c_2Esptree_2Elrnext_2E1(V2i_2E0))),c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V1k_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))) )
& ! [V3k_2E0: tyop_2Enum_2Enum,V4i_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Espt__acc_2E2(V4i_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V3k_2E0))) = c_2Esptree_2Espt__acc_2E2(c_2Earithmetic_2E_2B_2E2(V4i_2E0,c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Earithmetic_2EEVEN_2E1(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(V3k_2E0))),c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Esptree_2Elrnext_2E1(V4i_2E0)),c_2Esptree_2Elrnext_2E1(V4i_2E0))),c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(V3k_2E0)),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))) ) ) ).
tff(thm_2Esptree_2Espt__acc__def,axiom,
( ! [V0i_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Espt__acc_2E2(V0i_2E0,c_2Enum_2E0_2E0) = V0i_2E0 )
& ! [V1k_2E0: tyop_2Enum_2Enum,V2i_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Espt__acc_2E2(V2i_2E0,c_2Enum_2ESUC_2E1(V1k_2E0)) = c_2Esptree_2Espt__acc_2E2(c_2Earithmetic_2E_2B_2E2(V2i_2E0,c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Earithmetic_2EEVEN_2E1(c_2Enum_2ESUC_2E1(V1k_2E0)),c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Esptree_2Elrnext_2E1(V2i_2E0)),c_2Esptree_2Elrnext_2E1(V2i_2E0))),c_2Earithmetic_2EDIV_2E2(V1k_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))) ) ) ).
tff(thm_2Esptree_2Espt__acc__ind,axiom,
! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
( ( ! [V1i_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0,V1i_2E0),c_2Enum_2E0_2E0))
& ! [V2i_2E0: tyop_2Enum_2Enum,V3k_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0,c_2Earithmetic_2E_2B_2E2(V2i_2E0,c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Earithmetic_2EEVEN_2E1(c_2Enum_2ESUC_2E1(V3k_2E0)),c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Esptree_2Elrnext_2E1(V2i_2E0)),c_2Esptree_2Elrnext_2E1(V2i_2E0)))),c_2Earithmetic_2EDIV_2E2(V3k_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))
=> p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0,V2i_2E0),c_2Enum_2ESUC_2E1(V3k_2E0))) ) )
=> ! [V4v_2E0: tyop_2Enum_2Enum,V5v1_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),V0P_2E0,V4v_2E0),V5v1_2E0)) ) ).
tff(thm_2Esptree_2Edomain__delete,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Esptree_2Espt(A_27a),V1k_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Edomain_2E1(A_27a,c_2Esptree_2Edelete_2E2(A_27a,V1k_2E0,V0t_2E0)) = c_2Epred__set_2EDELETE_2E2(tyop_2Enum_2Enum,c_2Esptree_2Edomain_2E1(A_27a,V0t_2E0),V1k_2E0) ) ).
tff(thm_2Esptree_2Elookup__delete,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
( ! [V1k1_2E0: tyop_2Enum_2Enum,V2k2_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1k1_2E0),V2k2_2E0))
<=> ( V1k1_2E0 = V2k2_2E0 ) )
=> ! [V0t_2E0: tyop_2Esptree_2Espt(A_27a),V1k1_2E0: tyop_2Enum_2Enum,V2k2_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Elookup_2E2(A_27a,V1k1_2E0,c_2Esptree_2Edelete_2E2(A_27a,V2k2_2E0,V0t_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V1k1_2E0),V2k2_2E0),c_2Eoption_2ENONE_2E0(A_27a),c_2Esptree_2Elookup_2E2(A_27a,V1k1_2E0,V0t_2E0)) ) ) ).
tff(thm_2Esptree_2Edomain__fromList,axiom,
! [A_27a: $tType,V0l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Esptree_2Edomain_2E1(A_27a,c_2Esptree_2EfromList_2E1(A_27a,V0l_2E0)) = c_2Epred__set_2Ecount_2E1(c_2Elist_2ELENGTH_2E1(A_27a,V0l_2E0)) ) ).
tff(thm_2Esptree_2Edomain__sing,axiom,
! [A_27a: $tType,V0v_2E0: A_27a,V1k_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Edomain_2E1(A_27a,c_2Esptree_2Einsert_2E3(A_27a,V1k_2E0,V0v_2E0,c_2Esptree_2ELN_2E0(A_27a))) = c_2Epred__set_2EINSERT_2E2(tyop_2Enum_2Enum,V1k_2E0,c_2Epred__set_2EEMPTY_2E0(tyop_2Enum_2Enum)) ) ).
tff(thm_2Esptree_2Edomain__difference,axiom,
! [A_27a: $tType,A_27b: $tType,V0t1_2E0: tyop_2Esptree_2Espt(A_27a),V1t2_2E0: tyop_2Esptree_2Espt(A_27b)] : ( c_2Esptree_2Edomain_2E1(A_27a,c_2Esptree_2Edifference_2E2(A_27a,A_27b,V0t1_2E0,V1t2_2E0)) = c_2Epred__set_2EDIFF_2E2(tyop_2Enum_2Enum,c_2Esptree_2Edomain_2E1(A_27a,V0t1_2E0),c_2Esptree_2Edomain_2E1(A_27b,V1t2_2E0)) ) ).
tff(thm_2Esptree_2Edomain__insert,axiom,
! [A_27a: $tType,V0v_2E0: A_27a,V1t_2E0: tyop_2Esptree_2Espt(A_27a),V2k_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Edomain_2E1(A_27a,c_2Esptree_2Einsert_2E3(A_27a,V2k_2E0,V0v_2E0,V1t_2E0)) = c_2Epred__set_2EINSERT_2E2(tyop_2Enum_2Enum,V2k_2E0,c_2Esptree_2Edomain_2E1(A_27a,V1t_2E0)) ) ).
tff(thm_2Esptree_2Edomain__inter,axiom,
! [A_27a: $tType,A_27b: $tType,V0t2_2E0: tyop_2Esptree_2Espt(A_27b),V1t1_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Edomain_2E1(A_27a,c_2Esptree_2Einter_2E2(A_27a,A_27b,V1t1_2E0,V0t2_2E0)) = c_2Epred__set_2EINTER_2E2(tyop_2Enum_2Enum,c_2Esptree_2Edomain_2E1(A_27a,V1t1_2E0),c_2Esptree_2Edomain_2E1(A_27b,V0t2_2E0)) ) ).
tff(thm_2Esptree_2Edomain__union,axiom,
! [A_27a: $tType,V0t2_2E0: tyop_2Esptree_2Espt(A_27a),V1t1_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Edomain_2E1(A_27a,c_2Esptree_2Eunion_2E2(A_27a,V1t1_2E0,V0t2_2E0)) = c_2Epred__set_2EUNION_2E2(tyop_2Enum_2Enum,c_2Esptree_2Edomain_2E1(A_27a,V1t1_2E0),c_2Esptree_2Edomain_2E1(A_27a,V0t2_2E0)) ) ).
tff(thm_2Esptree_2Elookup__NONE__domain,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Esptree_2Espt(A_27a),V1k_2E0: tyop_2Enum_2Enum] :
( ( c_2Esptree_2Elookup_2E2(A_27a,V1k_2E0,V0t_2E0) = c_2Eoption_2ENONE_2E0(A_27a) )
<=> ~ p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V1k_2E0,c_2Esptree_2Edomain_2E1(A_27a,V0t_2E0))) ) ).
tff(thm_2Esptree_2Elookup__inter__alt,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Enum_2Enum,V1t2_2E0: tyop_2Esptree_2Espt(A_27b),V2t1_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Elookup_2E2(A_27a,V0x_2E0,c_2Esptree_2Einter_2E2(A_27a,A_27b,V2t1_2E0,V1t2_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V0x_2E0,c_2Esptree_2Edomain_2E1(A_27b,V1t2_2E0)),c_2Esptree_2Elookup_2E2(A_27a,V0x_2E0,V2t1_2E0),c_2Eoption_2ENONE_2E0(A_27a)) ) ).
tff(thm_2Esptree_2Edomain__lookup,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Esptree_2Espt(A_27a),V1k_2E0: tyop_2Enum_2Enum] :
( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V1k_2E0,c_2Esptree_2Edomain_2E1(A_27a,V0t_2E0)))
<=> ? [V2v_2E0: A_27a] : ( c_2Esptree_2Elookup_2E2(A_27a,V1k_2E0,V0t_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V2v_2E0) ) ) ).
tff(thm_2Esptree_2Elookup__fromList,axiom,
! [A_27a: $tType,V0n_2E0: tyop_2Enum_2Enum,V1l_2E0: tyop_2Elist_2Elist(A_27a)] : ( c_2Esptree_2Elookup_2E2(A_27a,V0n_2E0,c_2Esptree_2EfromList_2E1(A_27a,V1l_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),c_2Eprim__rec_2E_3C_2E2(V0n_2E0,c_2Elist_2ELENGTH_2E1(A_27a,V1l_2E0)),c_2Eoption_2ESOME_2E1(A_27a,c_2Elist_2EEL_2E2(A_27a,V0n_2E0,V1l_2E0)),c_2Eoption_2ENONE_2E0(A_27a)) ) ).
tff(thm_2Esptree_2Esize__insert,axiom,
! [A_27a: $tType,V0k_2E0: tyop_2Enum_2Enum,V1v_2E0: A_27a,V2m_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Esize_2E1(A_27a,c_2Esptree_2Einsert_2E3(A_27a,V0k_2E0,V1v_2E0,V2m_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V0k_2E0,c_2Esptree_2Edomain_2E1(A_27a,V2m_2E0)),c_2Esptree_2Esize_2E1(A_27a,V2m_2E0),c_2Earithmetic_2E_2B_2E2(c_2Esptree_2Esize_2E1(A_27a,V2m_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)))) ) ).
tff(thm_2Esptree_2Esubspt__domain,axiom,
! [V0t1_2E0: tyop_2Esptree_2Espt(tyop_2Eone_2Eone),V1t2_2E0: tyop_2Esptree_2Espt(tyop_2Eone_2Eone)] : ( c_2Esptree_2Esubspt_2E2(tyop_2Eone_2Eone,V0t1_2E0,V1t2_2E0) = c_2Epred__set_2ESUBSET_2E2(tyop_2Enum_2Enum,c_2Esptree_2Edomain_2E1(tyop_2Eone_2Eone,V0t1_2E0),c_2Esptree_2Edomain_2E1(tyop_2Eone_2Eone,V1t2_2E0)) ) ).
tff(thm_2Esptree_2Esubspt__lookup,axiom,
! [A_27a: $tType,V0t1_2E0: tyop_2Esptree_2Espt(A_27a),V1t2_2E0: tyop_2Esptree_2Espt(A_27a)] :
( p(c_2Esptree_2Esubspt_2E2(A_27a,V0t1_2E0,V1t2_2E0))
<=> ! [V2x_2E0: tyop_2Enum_2Enum,V3y_2E0: A_27a] :
( ( c_2Esptree_2Elookup_2E2(A_27a,V2x_2E0,V0t1_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V3y_2E0) )
=> ( c_2Esptree_2Elookup_2E2(A_27a,V2x_2E0,V1t2_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V3y_2E0) ) ) ) ).
tff(thm_2Esptree_2Esubspt__eq,axiom,
! [A_27a: $tType] :
( ! [V0t_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Esubspt_2E2(A_27a,c_2Esptree_2ELN_2E0(A_27a),V0t_2E0) = c_2Ebool_2ET_2E0 )
& ! [V1x_2E0: A_27a,V2t_2E0: tyop_2Esptree_2Espt(A_27a)] :
( p(c_2Esptree_2Esubspt_2E2(A_27a,c_2Esptree_2ELS_2E1(A_27a,V1x_2E0),V2t_2E0))
<=> ( c_2Esptree_2Espt__center_2E1(A_27a,V2t_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V1x_2E0) ) )
& ! [V3t1_2E0: tyop_2Esptree_2Espt(A_27a),V4t2_2E0: tyop_2Esptree_2Espt(A_27a),V5t_2E0: tyop_2Esptree_2Espt(A_27a)] :
( p(c_2Esptree_2Esubspt_2E2(A_27a,c_2Esptree_2EBN_2E2(A_27a,V3t1_2E0,V4t2_2E0),V5t_2E0))
<=> ( p(c_2Esptree_2Esubspt_2E2(A_27a,V3t1_2E0,c_2Esptree_2Espt__left_2E1(A_27a,V5t_2E0)))
& p(c_2Esptree_2Esubspt_2E2(A_27a,V4t2_2E0,c_2Esptree_2Espt__right_2E1(A_27a,V5t_2E0))) ) )
& ! [V6t1_2E0: tyop_2Esptree_2Espt(A_27a),V7x_2E0: A_27a,V8t2_2E0: tyop_2Esptree_2Espt(A_27a),V9t_2E0: tyop_2Esptree_2Espt(A_27a)] :
( p(c_2Esptree_2Esubspt_2E2(A_27a,c_2Esptree_2EBS_2E3(A_27a,V6t1_2E0,V7x_2E0,V8t2_2E0),V9t_2E0))
<=> ( ( c_2Esptree_2Espt__center_2E1(A_27a,V9t_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V7x_2E0) )
& p(c_2Esptree_2Esubspt_2E2(A_27a,V6t1_2E0,c_2Esptree_2Espt__left_2E1(A_27a,V9t_2E0)))
& p(c_2Esptree_2Esubspt_2E2(A_27a,V8t2_2E0,c_2Esptree_2Espt__right_2E1(A_27a,V9t_2E0))) ) ) ) ).
tff(thm_2Esptree_2Edatatype__spt,axiom,
! [A_27a: $tType,V0spt_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),tyop_2Emin_2Ebool))))] : p(c_2Ebool_2EDATATYPE_2E1(tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),tyop_2Emin_2Ebool,app_2E2(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),tyop_2Emin_2Ebool),app_2E2(tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),tyop_2Emin_2Ebool)),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Emin_2Efun(A_27a,tyop_2Esptree_2Espt(A_27a)),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a))),tyop_2Emin_2Efun(tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Esptree_2Espt(A_27a)))),tyop_2Emin_2Ebool))),V0spt_2E0,c_2Esptree_2ELN_2E0(A_27a)),c_2Esptree_2ELS_2E0(A_27a)),c_2Esptree_2EBN_2E0(A_27a)),c_2Esptree_2EBS_2E0(A_27a)))) ).
tff(thm_2Esptree_2Espt__11,axiom,
! [A_27a: $tType] :
( ! [V0a_2E0: A_27a,V1a_27_2E0: A_27a] :
( ( c_2Esptree_2ELS_2E1(A_27a,V0a_2E0) = c_2Esptree_2ELS_2E1(A_27a,V1a_27_2E0) )
<=> ( V0a_2E0 = V1a_27_2E0 ) )
& ! [V2a0_2E0: tyop_2Esptree_2Espt(A_27a),V3a1_2E0: tyop_2Esptree_2Espt(A_27a),V4a0_27_2E0: tyop_2Esptree_2Espt(A_27a),V5a1_27_2E0: tyop_2Esptree_2Espt(A_27a)] :
( ( c_2Esptree_2EBN_2E2(A_27a,V2a0_2E0,V3a1_2E0) = c_2Esptree_2EBN_2E2(A_27a,V4a0_27_2E0,V5a1_27_2E0) )
<=> ( ( V2a0_2E0 = V4a0_27_2E0 )
& ( V3a1_2E0 = V5a1_27_2E0 ) ) )
& ! [V6a0_2E0: tyop_2Esptree_2Espt(A_27a),V7a1_2E0: A_27a,V8a2_2E0: tyop_2Esptree_2Espt(A_27a),V9a0_27_2E0: tyop_2Esptree_2Espt(A_27a),V10a1_27_2E0: A_27a,V11a2_27_2E0: tyop_2Esptree_2Espt(A_27a)] :
( ( c_2Esptree_2EBS_2E3(A_27a,V6a0_2E0,V7a1_2E0,V8a2_2E0) = c_2Esptree_2EBS_2E3(A_27a,V9a0_27_2E0,V10a1_27_2E0,V11a2_27_2E0) )
<=> ( ( V6a0_2E0 = V9a0_27_2E0 )
& ( V7a1_2E0 = V10a1_27_2E0 )
& ( V8a2_2E0 = V11a2_27_2E0 ) ) ) ) ).
tff(thm_2Esptree_2Espt__distinct,axiom,
! [A_27a: $tType] :
( ! [V0a_2E0: A_27a] : ( c_2Esptree_2ELN_2E0(A_27a) != c_2Esptree_2ELS_2E1(A_27a,V0a_2E0) )
& ! [V1a1_2E0: tyop_2Esptree_2Espt(A_27a),V2a0_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2ELN_2E0(A_27a) != c_2Esptree_2EBN_2E2(A_27a,V2a0_2E0,V1a1_2E0) )
& ! [V3a2_2E0: tyop_2Esptree_2Espt(A_27a),V4a1_2E0: A_27a,V5a0_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2ELN_2E0(A_27a) != c_2Esptree_2EBS_2E3(A_27a,V5a0_2E0,V4a1_2E0,V3a2_2E0) )
& ! [V6a1_2E0: tyop_2Esptree_2Espt(A_27a),V7a0_2E0: tyop_2Esptree_2Espt(A_27a),V8a_2E0: A_27a] : ( c_2Esptree_2ELS_2E1(A_27a,V8a_2E0) != c_2Esptree_2EBN_2E2(A_27a,V7a0_2E0,V6a1_2E0) )
& ! [V9a2_2E0: tyop_2Esptree_2Espt(A_27a),V10a1_2E0: A_27a,V11a0_2E0: tyop_2Esptree_2Espt(A_27a),V12a_2E0: A_27a] : ( c_2Esptree_2ELS_2E1(A_27a,V12a_2E0) != c_2Esptree_2EBS_2E3(A_27a,V11a0_2E0,V10a1_2E0,V9a2_2E0) )
& ! [V13a2_2E0: tyop_2Esptree_2Espt(A_27a),V14a1_27_2E0: A_27a,V15a1_2E0: tyop_2Esptree_2Espt(A_27a),V16a0_27_2E0: tyop_2Esptree_2Espt(A_27a),V17a0_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2EBN_2E2(A_27a,V17a0_2E0,V15a1_2E0) != c_2Esptree_2EBS_2E3(A_27a,V16a0_27_2E0,V14a1_27_2E0,V13a2_2E0) ) ) ).
tff(thm_2Esptree_2Espt__nchotomy,axiom,
! [A_27a: $tType,V0ss_2E0: tyop_2Esptree_2Espt(A_27a)] :
( ( V0ss_2E0 = c_2Esptree_2ELN_2E0(A_27a) )
| ? [V1a_2E0: A_27a] : ( V0ss_2E0 = c_2Esptree_2ELS_2E1(A_27a,V1a_2E0) )
| ? [V2s_2E0: tyop_2Esptree_2Espt(A_27a),V3s0_2E0: tyop_2Esptree_2Espt(A_27a)] : ( V0ss_2E0 = c_2Esptree_2EBN_2E2(A_27a,V2s_2E0,V3s0_2E0) )
| ? [V4s_2E0: tyop_2Esptree_2Espt(A_27a),V5a_2E0: A_27a,V6s0_2E0: tyop_2Esptree_2Espt(A_27a)] : ( V0ss_2E0 = c_2Esptree_2EBS_2E3(A_27a,V4s_2E0,V5a_2E0,V6s0_2E0) ) ) ).
tff(thm_2Esptree_2Espt__Axiom,axiom,
! [A_27a: $tType,A_27b: $tType,V0f0_2E0: A_27b,V1f1_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V2f2_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)))),V3f3_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)))))] :
? [V4fn_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)] :
( ( app_2E2(tyop_2Esptree_2Espt(A_27a),A_27b,V4fn_2E0,c_2Esptree_2ELN_2E0(A_27a)) = V0f0_2E0 )
& ! [V5a_2E0: A_27a] : ( app_2E2(tyop_2Esptree_2Espt(A_27a),A_27b,V4fn_2E0,c_2Esptree_2ELS_2E1(A_27a,V5a_2E0)) = app_2E2(A_27a,A_27b,V1f1_2E0,V5a_2E0) )
& ! [V6a0_2E0: tyop_2Esptree_2Espt(A_27a),V7a1_2E0: tyop_2Esptree_2Espt(A_27a)] : ( app_2E2(tyop_2Esptree_2Espt(A_27a),A_27b,V4fn_2E0,c_2Esptree_2EBN_2E2(A_27a,V6a0_2E0,V7a1_2E0)) = app_2E2(A_27b,A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))),V2f2_2E0,V6a0_2E0),V7a1_2E0),app_2E2(tyop_2Esptree_2Espt(A_27a),A_27b,V4fn_2E0,V6a0_2E0)),app_2E2(tyop_2Esptree_2Espt(A_27a),A_27b,V4fn_2E0,V7a1_2E0)) )
& ! [V8a0_2E0: tyop_2Esptree_2Espt(A_27a),V9a1_2E0: A_27a,V10a2_2E0: tyop_2Esptree_2Espt(A_27a)] : ( app_2E2(tyop_2Esptree_2Espt(A_27a),A_27b,V4fn_2E0,c_2Esptree_2EBS_2E3(A_27a,V8a0_2E0,V9a1_2E0,V10a2_2E0)) = app_2E2(A_27b,A_27b,app_2E2(A_27b,tyop_2Emin_2Efun(A_27b,A_27b),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b))),app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27b,tyop_2Emin_2Efun(A_27b,A_27b)))),V3f3_2E0,V9a1_2E0),V8a0_2E0),V10a2_2E0),app_2E2(tyop_2Esptree_2Espt(A_27a),A_27b,V4fn_2E0,V8a0_2E0)),app_2E2(tyop_2Esptree_2Espt(A_27a),A_27b,V4fn_2E0,V10a2_2E0)) ) ) ).
tff(thm_2Esptree_2Espt__induction,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)] :
( ( p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Esptree_2ELN_2E0(A_27a)))
& ! [V1a_2E0: A_27a] : p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Esptree_2ELS_2E1(A_27a,V1a_2E0)))
& ! [V2s_2E0: tyop_2Esptree_2Espt(A_27a),V3s0_2E0: tyop_2Esptree_2Espt(A_27a)] :
( ( p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V2s_2E0))
& p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V3s0_2E0)) )
=> p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Esptree_2EBN_2E2(A_27a,V2s_2E0,V3s0_2E0))) )
& ! [V4s_2E0: tyop_2Esptree_2Espt(A_27a),V5s0_2E0: tyop_2Esptree_2Espt(A_27a)] :
( ( p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V4s_2E0))
& p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V5s0_2E0)) )
=> ! [V6a_2E0: A_27a] : p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,V0P_2E0,c_2Esptree_2EBS_2E3(A_27a,V4s_2E0,V6a_2E0,V5s0_2E0))) ) )
=> ! [V7s_2E0: tyop_2Esptree_2Espt(A_27a)] : p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,V0P_2E0,V7s_2E0)) ) ).
tff(thm_2Esptree_2Espt__case__cong,axiom,
! [A_27a: $tType,A_27b: $tType,V0v_27_2E0: A_27b,V1f2_27_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b))),V2f1_27_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),V3f_27_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V4M_2E0: tyop_2Esptree_2Espt(A_27a),V5M_27_2E0: tyop_2Esptree_2Espt(A_27a),V6v_2E0: A_27b,V7f_2E0: tyop_2Emin_2Efun(A_27a,A_27b),V8f1_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),V9f2_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)))] :
( ( ( V4M_2E0 = V5M_27_2E0 )
& ( ( V5M_27_2E0 = c_2Esptree_2ELN_2E0(A_27a) )
=> ( V6v_2E0 = V0v_27_2E0 ) )
& ! [V10a_2E0: A_27a] :
( ( V5M_27_2E0 = c_2Esptree_2ELS_2E1(A_27a,V10a_2E0) )
=> ( app_2E2(A_27a,A_27b,V7f_2E0,V10a_2E0) = app_2E2(A_27a,A_27b,V3f_27_2E0,V10a_2E0) ) )
& ! [V11a0_2E0: tyop_2Esptree_2Espt(A_27a),V12a1_2E0: tyop_2Esptree_2Espt(A_27a)] :
( ( V5M_27_2E0 = c_2Esptree_2EBN_2E2(A_27a,V11a0_2E0,V12a1_2E0) )
=> ( app_2E2(tyop_2Esptree_2Espt(A_27a),A_27b,app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b),V8f1_2E0,V11a0_2E0),V12a1_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),A_27b,app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b),V2f1_27_2E0,V11a0_2E0),V12a1_2E0) ) )
& ! [V13a0_2E0: tyop_2Esptree_2Espt(A_27a),V14a1_2E0: A_27a,V15a2_2E0: tyop_2Esptree_2Espt(A_27a)] :
( ( V5M_27_2E0 = c_2Esptree_2EBS_2E3(A_27a,V13a0_2E0,V14a1_2E0,V15a2_2E0) )
=> ( app_2E2(tyop_2Esptree_2Espt(A_27a),A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),V9f2_2E0,V13a0_2E0),V14a1_2E0),V15a2_2E0) = app_2E2(tyop_2Esptree_2Espt(A_27a),A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),V1f2_27_2E0,V13a0_2E0),V14a1_2E0),V15a2_2E0) ) ) )
=> ( c_2Esptree_2Espt__CASE_2E5(A_27a,A_27b,V4M_2E0,V6v_2E0,V7f_2E0,V8f1_2E0,V9f2_2E0) = c_2Esptree_2Espt__CASE_2E5(A_27a,A_27b,V5M_27_2E0,V0v_27_2E0,V3f_27_2E0,V2f1_27_2E0,V1f2_27_2E0) ) ) ).
tff(thm_2Esptree_2Espt__case__eq,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Esptree_2Espt(A_27a),V1v_27_2E0: A_27b,V2v_2E0: A_27b,V3f2_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b))),V4f1_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),V5f_2E0: tyop_2Emin_2Efun(A_27a,A_27b)] :
( ( c_2Esptree_2Espt__CASE_2E5(A_27a,A_27b,V0x_2E0,V2v_2E0,V5f_2E0,V4f1_2E0,V3f2_2E0) = V1v_27_2E0 )
<=> ( ( ( V0x_2E0 = c_2Esptree_2ELN_2E0(A_27a) )
& ( V2v_2E0 = V1v_27_2E0 ) )
| ? [V6a_2E0: A_27a] :
( ( V0x_2E0 = c_2Esptree_2ELS_2E1(A_27a,V6a_2E0) )
& ( app_2E2(A_27a,A_27b,V5f_2E0,V6a_2E0) = V1v_27_2E0 ) )
| ? [V7s_2E0: tyop_2Esptree_2Espt(A_27a),V8s0_2E0: tyop_2Esptree_2Espt(A_27a)] :
( ( V0x_2E0 = c_2Esptree_2EBN_2E2(A_27a,V7s_2E0,V8s0_2E0) )
& ( app_2E2(tyop_2Esptree_2Espt(A_27a),A_27b,app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b),V4f1_2E0,V7s_2E0),V8s0_2E0) = V1v_27_2E0 ) )
| ? [V9s_2E0: tyop_2Esptree_2Espt(A_27a),V10a_2E0: A_27a,V11s0_2E0: tyop_2Esptree_2Espt(A_27a)] :
( ( V0x_2E0 = c_2Esptree_2EBS_2E3(A_27a,V9s_2E0,V10a_2E0,V11s0_2E0) )
& ( app_2E2(tyop_2Esptree_2Espt(A_27a),A_27b,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),A_27b)),V3f2_2E0,V9s_2E0),V10a_2E0),V11s0_2E0) = V1v_27_2E0 ) ) ) ) ).
tff(thm_2Esptree_2Elookup__ind,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool))] :
( ( ! [V1k_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),V0P_2E0,V1k_2E0),c_2Esptree_2ELN_2E0(A_27a)))
& ! [V2k_2E0: tyop_2Enum_2Enum,V3a_2E0: A_27a] : p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),V0P_2E0,V2k_2E0),c_2Esptree_2ELS_2E1(A_27a,V3a_2E0)))
& ! [V4k_2E0: tyop_2Enum_2Enum,V5t1_2E0: tyop_2Esptree_2Espt(A_27a),V6t2_2E0: tyop_2Esptree_2Espt(A_27a)] :
( ( ( V4k_2E0 != c_2Enum_2E0_2E0 )
=> p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),V0P_2E0,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V4k_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2Ebool_2ECOND_2E3(tyop_2Esptree_2Espt(A_27a),c_2Earithmetic_2EEVEN_2E1(V4k_2E0),V5t1_2E0,V6t2_2E0))) )
=> p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),V0P_2E0,V4k_2E0),c_2Esptree_2EBN_2E2(A_27a,V5t1_2E0,V6t2_2E0))) )
& ! [V7k_2E0: tyop_2Enum_2Enum,V8t1_2E0: tyop_2Esptree_2Espt(A_27a),V9a_2E0: A_27a,V10t2_2E0: tyop_2Esptree_2Espt(A_27a)] :
( ( ( V7k_2E0 != c_2Enum_2E0_2E0 )
=> p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),V0P_2E0,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V7k_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))),c_2Ebool_2ECOND_2E3(tyop_2Esptree_2Espt(A_27a),c_2Earithmetic_2EEVEN_2E1(V7k_2E0),V8t1_2E0,V10t2_2E0))) )
=> p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),V0P_2E0,V7k_2E0),c_2Esptree_2EBS_2E3(A_27a,V8t1_2E0,V9a_2E0,V10t2_2E0))) ) )
=> ! [V11v_2E0: tyop_2Enum_2Enum,V12v1_2E0: tyop_2Esptree_2Espt(A_27a)] : p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),V0P_2E0,V11v_2E0),V12v1_2E0)) ) ).
tff(thm_2Esptree_2Elookup__def,axiom,
! [A_27a: $tType,F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( ! [V8k_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F2_2E0,V8k_2E0))
<=> ( V8k_2E0 = c_2Enum_2E0_2E0 ) )
=> ( ! [V5k_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F1_2E0,V5k_2E0))
<=> ( V5k_2E0 = c_2Enum_2E0_2E0 ) )
=> ( ! [V1k_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V1k_2E0))
<=> ( V1k_2E0 = c_2Enum_2E0_2E0 ) )
=> ( ! [V0k_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Elookup_2E2(A_27a,V0k_2E0,c_2Esptree_2ELN_2E0(A_27a)) = c_2Eoption_2ENONE_2E0(A_27a) )
& ! [V1k_2E0: tyop_2Enum_2Enum,V2a_2E0: A_27a] : ( c_2Esptree_2Elookup_2E2(A_27a,V1k_2E0,c_2Esptree_2ELS_2E1(A_27a,V2a_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V1k_2E0),c_2Eoption_2ESOME_2E1(A_27a,V2a_2E0),c_2Eoption_2ENONE_2E0(A_27a)) )
& ! [V3t2_2E0: tyop_2Esptree_2Espt(A_27a),V4t1_2E0: tyop_2Esptree_2Espt(A_27a),V5k_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Elookup_2E2(A_27a,V5k_2E0,c_2Esptree_2EBN_2E2(A_27a,V4t1_2E0,V3t2_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F1_2E0,V5k_2E0),c_2Eoption_2ENONE_2E0(A_27a),c_2Esptree_2Elookup_2E2(A_27a,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V5k_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Ebool_2ECOND_2E3(tyop_2Esptree_2Espt(A_27a),c_2Earithmetic_2EEVEN_2E1(V5k_2E0),V4t1_2E0,V3t2_2E0))) )
& ! [V6t2_2E0: tyop_2Esptree_2Espt(A_27a),V7t1_2E0: tyop_2Esptree_2Espt(A_27a),V8k_2E0: tyop_2Enum_2Enum,V9a_2E0: A_27a] : ( c_2Esptree_2Elookup_2E2(A_27a,V8k_2E0,c_2Esptree_2EBS_2E3(A_27a,V7t1_2E0,V9a_2E0,V6t2_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F2_2E0,V8k_2E0),c_2Eoption_2ESOME_2E1(A_27a,V9a_2E0),c_2Esptree_2Elookup_2E2(A_27a,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V8k_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Ebool_2ECOND_2E3(tyop_2Esptree_2Espt(A_27a),c_2Earithmetic_2EEVEN_2E1(V8k_2E0),V7t1_2E0,V6t2_2E0))) ) ) ) ) ) ).
tff(thm_2Esptree_2Einsert__ind,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)))] :
( ( ! [V1k_2E0: tyop_2Enum_2Enum,V2a_2E0: A_27a] :
( ( ( ( ( V1k_2E0 != c_2Enum_2E0_2E0 )
& p(c_2Earithmetic_2EEVEN_2E1(V1k_2E0)) )
=> p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V1k_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))),V2a_2E0),c_2Esptree_2ELN_2E0(A_27a))) )
& ( ( ( V1k_2E0 != c_2Enum_2E0_2E0 )
& ~ p(c_2Earithmetic_2EEVEN_2E1(V1k_2E0)) )
=> p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V1k_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))),V2a_2E0),c_2Esptree_2ELN_2E0(A_27a))) ) )
=> p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V1k_2E0),V2a_2E0),c_2Esptree_2ELN_2E0(A_27a))) )
& ! [V3k_2E0: tyop_2Enum_2Enum,V4a_2E0: A_27a,V5a_27_2E0: A_27a] :
( ( ( ( ( V3k_2E0 != c_2Enum_2E0_2E0 )
& p(c_2Earithmetic_2EEVEN_2E1(V3k_2E0)) )
=> p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V3k_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))),V4a_2E0),c_2Esptree_2ELN_2E0(A_27a))) )
& ( ( ( V3k_2E0 != c_2Enum_2E0_2E0 )
& ~ p(c_2Earithmetic_2EEVEN_2E1(V3k_2E0)) )
=> p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V3k_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))),V4a_2E0),c_2Esptree_2ELN_2E0(A_27a))) ) )
=> p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V3k_2E0),V4a_2E0),c_2Esptree_2ELS_2E1(A_27a,V5a_27_2E0))) )
& ! [V6k_2E0: tyop_2Enum_2Enum,V7a_2E0: A_27a,V8t1_2E0: tyop_2Esptree_2Espt(A_27a),V9t2_2E0: tyop_2Esptree_2Espt(A_27a)] :
( ( ( ( ( V6k_2E0 != c_2Enum_2E0_2E0 )
& p(c_2Earithmetic_2EEVEN_2E1(V6k_2E0)) )
=> p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V6k_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))),V7a_2E0),V8t1_2E0)) )
& ( ( ( V6k_2E0 != c_2Enum_2E0_2E0 )
& ~ p(c_2Earithmetic_2EEVEN_2E1(V6k_2E0)) )
=> p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V6k_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))),V7a_2E0),V9t2_2E0)) ) )
=> p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V6k_2E0),V7a_2E0),c_2Esptree_2EBN_2E2(A_27a,V8t1_2E0,V9t2_2E0))) )
& ! [V10k_2E0: tyop_2Enum_2Enum,V11a_2E0: A_27a,V12t1_2E0: tyop_2Esptree_2Espt(A_27a),V13a_27_2E0: A_27a,V14t2_2E0: tyop_2Esptree_2Espt(A_27a)] :
( ( ( ( ( V10k_2E0 != c_2Enum_2E0_2E0 )
& p(c_2Earithmetic_2EEVEN_2E1(V10k_2E0)) )
=> p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V10k_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))),V11a_2E0),V12t1_2E0)) )
& ( ( ( V10k_2E0 != c_2Enum_2E0_2E0 )
& ~ p(c_2Earithmetic_2EEVEN_2E1(V10k_2E0)) )
=> p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V10k_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))),V11a_2E0),V14t2_2E0)) ) )
=> p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V10k_2E0),V11a_2E0),c_2Esptree_2EBS_2E3(A_27a,V12t1_2E0,V13a_27_2E0,V14t2_2E0))) ) )
=> ! [V15v_2E0: tyop_2Enum_2Enum,V16v1_2E0: A_27a,V17v2_2E0: tyop_2Esptree_2Espt(A_27a)] : p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V15v_2E0),V16v1_2E0),V17v2_2E0)) ) ).
tff(thm_2Esptree_2Einsert__def,axiom,
! [A_27a: $tType,F3_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F2_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( ! [V11k_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F3_2E0,V11k_2E0))
<=> ( V11k_2E0 = c_2Enum_2E0_2E0 ) )
=> ( ! [V7k_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F2_2E0,V7k_2E0))
<=> ( V7k_2E0 = c_2Enum_2E0_2E0 ) )
=> ( ! [V2k_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F1_2E0,V2k_2E0))
<=> ( V2k_2E0 = c_2Enum_2E0_2E0 ) )
=> ( ! [V0k_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V0k_2E0))
<=> ( V0k_2E0 = c_2Enum_2E0_2E0 ) )
=> ( ! [V0k_2E0: tyop_2Enum_2Enum,V1a_2E0: A_27a] : ( c_2Esptree_2Einsert_2E3(A_27a,V0k_2E0,V1a_2E0,c_2Esptree_2ELN_2E0(A_27a)) = c_2Ebool_2ECOND_2E3(tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V0k_2E0),c_2Esptree_2ELS_2E1(A_27a,V1a_2E0),c_2Ebool_2ECOND_2E3(tyop_2Esptree_2Espt(A_27a),c_2Earithmetic_2EEVEN_2E1(V0k_2E0),c_2Esptree_2EBN_2E2(A_27a,c_2Esptree_2Einsert_2E3(A_27a,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V0k_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),V1a_2E0,c_2Esptree_2ELN_2E0(A_27a)),c_2Esptree_2ELN_2E0(A_27a)),c_2Esptree_2EBN_2E2(A_27a,c_2Esptree_2ELN_2E0(A_27a),c_2Esptree_2Einsert_2E3(A_27a,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V0k_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),V1a_2E0,c_2Esptree_2ELN_2E0(A_27a))))) )
& ! [V2k_2E0: tyop_2Enum_2Enum,V3a_27_2E0: A_27a,V4a_2E0: A_27a] : ( c_2Esptree_2Einsert_2E3(A_27a,V2k_2E0,V4a_2E0,c_2Esptree_2ELS_2E1(A_27a,V3a_27_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F1_2E0,V2k_2E0),c_2Esptree_2ELS_2E1(A_27a,V4a_2E0),c_2Ebool_2ECOND_2E3(tyop_2Esptree_2Espt(A_27a),c_2Earithmetic_2EEVEN_2E1(V2k_2E0),c_2Esptree_2EBS_2E3(A_27a,c_2Esptree_2Einsert_2E3(A_27a,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V2k_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),V4a_2E0,c_2Esptree_2ELN_2E0(A_27a)),V3a_27_2E0,c_2Esptree_2ELN_2E0(A_27a)),c_2Esptree_2EBS_2E3(A_27a,c_2Esptree_2ELN_2E0(A_27a),V3a_27_2E0,c_2Esptree_2Einsert_2E3(A_27a,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V2k_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),V4a_2E0,c_2Esptree_2ELN_2E0(A_27a))))) )
& ! [V5t2_2E0: tyop_2Esptree_2Espt(A_27a),V6t1_2E0: tyop_2Esptree_2Espt(A_27a),V7k_2E0: tyop_2Enum_2Enum,V8a_2E0: A_27a] : ( c_2Esptree_2Einsert_2E3(A_27a,V7k_2E0,V8a_2E0,c_2Esptree_2EBN_2E2(A_27a,V6t1_2E0,V5t2_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F2_2E0,V7k_2E0),c_2Esptree_2EBS_2E3(A_27a,V6t1_2E0,V8a_2E0,V5t2_2E0),c_2Ebool_2ECOND_2E3(tyop_2Esptree_2Espt(A_27a),c_2Earithmetic_2EEVEN_2E1(V7k_2E0),c_2Esptree_2EBN_2E2(A_27a,c_2Esptree_2Einsert_2E3(A_27a,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V7k_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),V8a_2E0,V6t1_2E0),V5t2_2E0),c_2Esptree_2EBN_2E2(A_27a,V6t1_2E0,c_2Esptree_2Einsert_2E3(A_27a,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V7k_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),V8a_2E0,V5t2_2E0)))) )
& ! [V9t2_2E0: tyop_2Esptree_2Espt(A_27a),V10t1_2E0: tyop_2Esptree_2Espt(A_27a),V11k_2E0: tyop_2Enum_2Enum,V12a_27_2E0: A_27a,V13a_2E0: A_27a] : ( c_2Esptree_2Einsert_2E3(A_27a,V11k_2E0,V13a_2E0,c_2Esptree_2EBS_2E3(A_27a,V10t1_2E0,V12a_27_2E0,V9t2_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Esptree_2Espt(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F3_2E0,V11k_2E0),c_2Esptree_2EBS_2E3(A_27a,V10t1_2E0,V13a_2E0,V9t2_2E0),c_2Ebool_2ECOND_2E3(tyop_2Esptree_2Espt(A_27a),c_2Earithmetic_2EEVEN_2E1(V11k_2E0),c_2Esptree_2EBS_2E3(A_27a,c_2Esptree_2Einsert_2E3(A_27a,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V11k_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),V13a_2E0,V10t1_2E0),V12a_27_2E0,V9t2_2E0),c_2Esptree_2EBS_2E3(A_27a,V10t1_2E0,V12a_27_2E0,c_2Esptree_2Einsert_2E3(A_27a,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V11k_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),V13a_2E0,V9t2_2E0)))) ) ) ) ) ) ) ).
tff(thm_2Esptree_2Emk__BN__ind,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool))] :
( ( p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),V0P_2E0,c_2Esptree_2ELN_2E0(A_27a)),c_2Esptree_2ELN_2E0(A_27a)))
& ! [V1v14_2E0: A_27a] : p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),V0P_2E0,c_2Esptree_2ELN_2E0(A_27a)),c_2Esptree_2ELS_2E1(A_27a,V1v14_2E0)))
& ! [V2v15_2E0: tyop_2Esptree_2Espt(A_27a),V3v16_2E0: tyop_2Esptree_2Espt(A_27a)] : p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),V0P_2E0,c_2Esptree_2ELN_2E0(A_27a)),c_2Esptree_2EBN_2E2(A_27a,V2v15_2E0,V3v16_2E0)))
& ! [V4v17_2E0: tyop_2Esptree_2Espt(A_27a),V5v18_2E0: A_27a,V6v19_2E0: tyop_2Esptree_2Espt(A_27a)] : p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),V0P_2E0,c_2Esptree_2ELN_2E0(A_27a)),c_2Esptree_2EBS_2E3(A_27a,V4v17_2E0,V5v18_2E0,V6v19_2E0)))
& ! [V7v2_2E0: A_27a,V8t2_2E0: tyop_2Esptree_2Espt(A_27a)] : p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),V0P_2E0,c_2Esptree_2ELS_2E1(A_27a,V7v2_2E0)),V8t2_2E0))
& ! [V9v3_2E0: tyop_2Esptree_2Espt(A_27a),V10v4_2E0: tyop_2Esptree_2Espt(A_27a),V11t2_2E0: tyop_2Esptree_2Espt(A_27a)] : p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),V0P_2E0,c_2Esptree_2EBN_2E2(A_27a,V9v3_2E0,V10v4_2E0)),V11t2_2E0))
& ! [V12v5_2E0: tyop_2Esptree_2Espt(A_27a),V13v6_2E0: A_27a,V14v7_2E0: tyop_2Esptree_2Espt(A_27a),V15t2_2E0: tyop_2Esptree_2Espt(A_27a)] : p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),V0P_2E0,c_2Esptree_2EBS_2E3(A_27a,V12v5_2E0,V13v6_2E0,V14v7_2E0)),V15t2_2E0)) )
=> ! [V16v_2E0: tyop_2Esptree_2Espt(A_27a),V17v1_2E0: tyop_2Esptree_2Espt(A_27a)] : p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),V0P_2E0,V16v_2E0),V17v1_2E0)) ) ).
tff(thm_2Esptree_2Emk__BN__def,axiom,
! [A_27a: $tType,V0v7_2E0: tyop_2Esptree_2Espt(A_27a),V1v6_2E0: A_27a,V2v5_2E0: tyop_2Esptree_2Espt(A_27a),V3v4_2E0: tyop_2Esptree_2Espt(A_27a),V4v3_2E0: tyop_2Esptree_2Espt(A_27a),V5v2_2E0: A_27a,V6v19_2E0: tyop_2Esptree_2Espt(A_27a),V7v18_2E0: A_27a,V8v17_2E0: tyop_2Esptree_2Espt(A_27a),V9v16_2E0: tyop_2Esptree_2Espt(A_27a),V10v15_2E0: tyop_2Esptree_2Espt(A_27a),V11v14_2E0: A_27a,V12t2_2E0: tyop_2Esptree_2Espt(A_27a)] :
( ( c_2Esptree_2Emk__BN_2E2(A_27a,c_2Esptree_2ELN_2E0(A_27a),c_2Esptree_2ELN_2E0(A_27a)) = c_2Esptree_2ELN_2E0(A_27a) )
& ( c_2Esptree_2Emk__BN_2E2(A_27a,c_2Esptree_2ELN_2E0(A_27a),c_2Esptree_2ELS_2E1(A_27a,V11v14_2E0)) = c_2Esptree_2EBN_2E2(A_27a,c_2Esptree_2ELN_2E0(A_27a),c_2Esptree_2ELS_2E1(A_27a,V11v14_2E0)) )
& ( c_2Esptree_2Emk__BN_2E2(A_27a,c_2Esptree_2ELN_2E0(A_27a),c_2Esptree_2EBN_2E2(A_27a,V10v15_2E0,V9v16_2E0)) = c_2Esptree_2EBN_2E2(A_27a,c_2Esptree_2ELN_2E0(A_27a),c_2Esptree_2EBN_2E2(A_27a,V10v15_2E0,V9v16_2E0)) )
& ( c_2Esptree_2Emk__BN_2E2(A_27a,c_2Esptree_2ELN_2E0(A_27a),c_2Esptree_2EBS_2E3(A_27a,V8v17_2E0,V7v18_2E0,V6v19_2E0)) = c_2Esptree_2EBN_2E2(A_27a,c_2Esptree_2ELN_2E0(A_27a),c_2Esptree_2EBS_2E3(A_27a,V8v17_2E0,V7v18_2E0,V6v19_2E0)) )
& ( c_2Esptree_2Emk__BN_2E2(A_27a,c_2Esptree_2ELS_2E1(A_27a,V5v2_2E0),V12t2_2E0) = c_2Esptree_2EBN_2E2(A_27a,c_2Esptree_2ELS_2E1(A_27a,V5v2_2E0),V12t2_2E0) )
& ( c_2Esptree_2Emk__BN_2E2(A_27a,c_2Esptree_2EBN_2E2(A_27a,V4v3_2E0,V3v4_2E0),V12t2_2E0) = c_2Esptree_2EBN_2E2(A_27a,c_2Esptree_2EBN_2E2(A_27a,V4v3_2E0,V3v4_2E0),V12t2_2E0) )
& ( c_2Esptree_2Emk__BN_2E2(A_27a,c_2Esptree_2EBS_2E3(A_27a,V2v5_2E0,V1v6_2E0,V0v7_2E0),V12t2_2E0) = c_2Esptree_2EBN_2E2(A_27a,c_2Esptree_2EBS_2E3(A_27a,V2v5_2E0,V1v6_2E0,V0v7_2E0),V12t2_2E0) ) ) ).
tff(thm_2Esptree_2Emk__BS__ind,axiom,
! [A_27a: $tType,V0P_2E0: tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)))] :
( ( ! [V1x_2E0: A_27a] : p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,c_2Esptree_2ELN_2E0(A_27a)),V1x_2E0),c_2Esptree_2ELN_2E0(A_27a)))
& ! [V2v16_2E0: A_27a,V3x_2E0: A_27a] : p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,c_2Esptree_2ELS_2E1(A_27a,V2v16_2E0)),V3x_2E0),c_2Esptree_2ELN_2E0(A_27a)))
& ! [V4v17_2E0: tyop_2Esptree_2Espt(A_27a),V5v18_2E0: tyop_2Esptree_2Espt(A_27a),V6x_2E0: A_27a] : p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,c_2Esptree_2EBN_2E2(A_27a,V4v17_2E0,V5v18_2E0)),V6x_2E0),c_2Esptree_2ELN_2E0(A_27a)))
& ! [V7v19_2E0: tyop_2Esptree_2Espt(A_27a),V8v20_2E0: A_27a,V9v21_2E0: tyop_2Esptree_2Espt(A_27a),V10x_2E0: A_27a] : p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,c_2Esptree_2EBS_2E3(A_27a,V7v19_2E0,V8v20_2E0,V9v21_2E0)),V10x_2E0),c_2Esptree_2ELN_2E0(A_27a)))
& ! [V11t1_2E0: tyop_2Esptree_2Espt(A_27a),V12x_2E0: A_27a,V13v4_2E0: A_27a] : p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V11t1_2E0),V12x_2E0),c_2Esptree_2ELS_2E1(A_27a,V13v4_2E0)))
& ! [V14t1_2E0: tyop_2Esptree_2Espt(A_27a),V15x_2E0: A_27a,V16v5_2E0: tyop_2Esptree_2Espt(A_27a),V17v6_2E0: tyop_2Esptree_2Espt(A_27a)] : p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V14t1_2E0),V15x_2E0),c_2Esptree_2EBN_2E2(A_27a,V16v5_2E0,V17v6_2E0)))
& ! [V18t1_2E0: tyop_2Esptree_2Espt(A_27a),V19x_2E0: A_27a,V20v7_2E0: tyop_2Esptree_2Espt(A_27a),V21v8_2E0: A_27a,V22v9_2E0: tyop_2Esptree_2Espt(A_27a)] : p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V18t1_2E0),V19x_2E0),c_2Esptree_2EBS_2E3(A_27a,V20v7_2E0,V21v8_2E0,V22v9_2E0))) )
=> ! [V23v_2E0: tyop_2Esptree_2Espt(A_27a),V24v1_2E0: A_27a,V25v2_2E0: tyop_2Esptree_2Espt(A_27a)] : p(app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool,app_2E2(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Ebool)),V0P_2E0,V23v_2E0),V24v1_2E0),V25v2_2E0)) ) ).
tff(thm_2Esptree_2Emk__BS__def,axiom,
! [A_27a: $tType,V0x_2E0: A_27a,V1v9_2E0: tyop_2Esptree_2Espt(A_27a),V2v8_2E0: A_27a,V3v7_2E0: tyop_2Esptree_2Espt(A_27a),V4v6_2E0: tyop_2Esptree_2Espt(A_27a),V5v5_2E0: tyop_2Esptree_2Espt(A_27a),V6v4_2E0: A_27a,V7v21_2E0: tyop_2Esptree_2Espt(A_27a),V8v20_2E0: A_27a,V9v19_2E0: tyop_2Esptree_2Espt(A_27a),V10v18_2E0: tyop_2Esptree_2Espt(A_27a),V11v17_2E0: tyop_2Esptree_2Espt(A_27a),V12v16_2E0: A_27a,V13t1_2E0: tyop_2Esptree_2Espt(A_27a)] :
( ( c_2Esptree_2Emk__BS_2E3(A_27a,c_2Esptree_2ELN_2E0(A_27a),V0x_2E0,c_2Esptree_2ELN_2E0(A_27a)) = c_2Esptree_2ELS_2E1(A_27a,V0x_2E0) )
& ( c_2Esptree_2Emk__BS_2E3(A_27a,c_2Esptree_2ELS_2E1(A_27a,V12v16_2E0),V0x_2E0,c_2Esptree_2ELN_2E0(A_27a)) = c_2Esptree_2EBS_2E3(A_27a,c_2Esptree_2ELS_2E1(A_27a,V12v16_2E0),V0x_2E0,c_2Esptree_2ELN_2E0(A_27a)) )
& ( c_2Esptree_2Emk__BS_2E3(A_27a,c_2Esptree_2EBN_2E2(A_27a,V11v17_2E0,V10v18_2E0),V0x_2E0,c_2Esptree_2ELN_2E0(A_27a)) = c_2Esptree_2EBS_2E3(A_27a,c_2Esptree_2EBN_2E2(A_27a,V11v17_2E0,V10v18_2E0),V0x_2E0,c_2Esptree_2ELN_2E0(A_27a)) )
& ( c_2Esptree_2Emk__BS_2E3(A_27a,c_2Esptree_2EBS_2E3(A_27a,V9v19_2E0,V8v20_2E0,V7v21_2E0),V0x_2E0,c_2Esptree_2ELN_2E0(A_27a)) = c_2Esptree_2EBS_2E3(A_27a,c_2Esptree_2EBS_2E3(A_27a,V9v19_2E0,V8v20_2E0,V7v21_2E0),V0x_2E0,c_2Esptree_2ELN_2E0(A_27a)) )
& ( c_2Esptree_2Emk__BS_2E3(A_27a,V13t1_2E0,V0x_2E0,c_2Esptree_2ELS_2E1(A_27a,V6v4_2E0)) = c_2Esptree_2EBS_2E3(A_27a,V13t1_2E0,V0x_2E0,c_2Esptree_2ELS_2E1(A_27a,V6v4_2E0)) )
& ( c_2Esptree_2Emk__BS_2E3(A_27a,V13t1_2E0,V0x_2E0,c_2Esptree_2EBN_2E2(A_27a,V5v5_2E0,V4v6_2E0)) = c_2Esptree_2EBS_2E3(A_27a,V13t1_2E0,V0x_2E0,c_2Esptree_2EBN_2E2(A_27a,V5v5_2E0,V4v6_2E0)) )
& ( c_2Esptree_2Emk__BS_2E3(A_27a,V13t1_2E0,V0x_2E0,c_2Esptree_2EBS_2E3(A_27a,V3v7_2E0,V2v8_2E0,V1v9_2E0)) = c_2Esptree_2EBS_2E3(A_27a,V13t1_2E0,V0x_2E0,c_2Esptree_2EBS_2E3(A_27a,V3v7_2E0,V2v8_2E0,V1v9_2E0)) ) ) ).
tff(thm_2Esptree_2Einsert__notEmpty,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Esptree_2Espt(A_27a),V1k_2E0: tyop_2Enum_2Enum,V2a_2E0: A_27a] : ( c_2Esptree_2Einsert_2E3(A_27a,V1k_2E0,V2a_2E0,V0t_2E0) != c_2Esptree_2ELN_2E0(A_27a) ) ).
tff(thm_2Esptree_2Ewf__insert,axiom,
! [A_27a: $tType,V0k_2E0: tyop_2Enum_2Enum,V1a_2E0: A_27a,V2t_2E0: tyop_2Esptree_2Espt(A_27a)] :
( p(c_2Esptree_2Ewf_2E1(A_27a,V2t_2E0))
=> p(c_2Esptree_2Ewf_2E1(A_27a,c_2Esptree_2Einsert_2E3(A_27a,V0k_2E0,V1a_2E0,V2t_2E0))) ) ).
tff(thm_2Esptree_2Ewf__delete,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Esptree_2Espt(A_27a),V1k_2E0: tyop_2Enum_2Enum] :
( p(c_2Esptree_2Ewf_2E1(A_27a,V0t_2E0))
=> p(c_2Esptree_2Ewf_2E1(A_27a,c_2Esptree_2Edelete_2E2(A_27a,V1k_2E0,V0t_2E0))) ) ).
tff(thm_2Esptree_2Elookup__insert1,axiom,
! [A_27a: $tType,V0k_2E0: tyop_2Enum_2Enum,V1a_2E0: A_27a,V2t_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Elookup_2E2(A_27a,V0k_2E0,c_2Esptree_2Einsert_2E3(A_27a,V0k_2E0,V1a_2E0,V2t_2E0)) = c_2Eoption_2ESOME_2E1(A_27a,V1a_2E0) ) ).
tff(thm_2Esptree_2Elookup__insert,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool))] :
( ! [V3k1_2E0: tyop_2Enum_2Enum,V0k2_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V3k1_2E0),V0k2_2E0))
<=> ( V3k1_2E0 = V0k2_2E0 ) )
=> ! [V0k2_2E0: tyop_2Enum_2Enum,V1v_2E0: A_27a,V2t_2E0: tyop_2Esptree_2Espt(A_27a),V3k1_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Elookup_2E2(A_27a,V3k1_2E0,c_2Esptree_2Einsert_2E3(A_27a,V0k2_2E0,V1v_2E0,V2t_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool),F0_2E0,V3k1_2E0),V0k2_2E0),c_2Eoption_2ESOME_2E1(A_27a,V1v_2E0),c_2Esptree_2Elookup_2E2(A_27a,V3k1_2E0,V2t_2E0)) ) ) ).
tff(thm_2Esptree_2EisEmpty__union,axiom,
! [A_27a: $tType,V0m2_2E0: tyop_2Esptree_2Espt(A_27a),V1m1_2E0: tyop_2Esptree_2Espt(A_27a)] :
( ( c_2Esptree_2Eunion_2E2(A_27a,V1m1_2E0,V0m2_2E0) = c_2Esptree_2ELN_2E0(A_27a) )
<=> ( ( V1m1_2E0 = c_2Esptree_2ELN_2E0(A_27a) )
& ( V0m2_2E0 = c_2Esptree_2ELN_2E0(A_27a) ) ) ) ).
tff(thm_2Esptree_2Ewf__union,axiom,
! [A_27a: $tType,V0m1_2E0: tyop_2Esptree_2Espt(A_27a),V1m2_2E0: tyop_2Esptree_2Espt(A_27a)] :
( ( p(c_2Esptree_2Ewf_2E1(A_27a,V0m1_2E0))
& p(c_2Esptree_2Ewf_2E1(A_27a,V1m2_2E0)) )
=> p(c_2Esptree_2Ewf_2E1(A_27a,c_2Esptree_2Eunion_2E2(A_27a,V0m1_2E0,V1m2_2E0))) ) ).
tff(thm_2Esptree_2Elookup__union,axiom,
! [A_27a: $tType,F0_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))] :
( ! [V3v_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27a),F0_2E0,V3v_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V3v_2E0) )
=> ! [V0m1_2E0: tyop_2Esptree_2Espt(A_27a),V1m2_2E0: tyop_2Esptree_2Espt(A_27a),V2k_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Elookup_2E2(A_27a,V2k_2E0,c_2Esptree_2Eunion_2E2(A_27a,V0m1_2E0,V1m2_2E0)) = c_2Eoption_2Eoption__CASE_2E3(A_27a,tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(A_27a,V2k_2E0,V0m1_2E0),c_2Esptree_2Elookup_2E2(A_27a,V2k_2E0,V1m2_2E0),F0_2E0) ) ) ).
tff(thm_2Esptree_2Ewf__inter,axiom,
! [A_27a: $tType,A_27b: $tType,V0m1_2E0: tyop_2Esptree_2Espt(A_27a),V1m2_2E0: tyop_2Esptree_2Espt(A_27b)] : p(c_2Esptree_2Ewf_2E1(A_27a,c_2Esptree_2Einter_2E2(A_27a,A_27b,V0m1_2E0,V1m2_2E0))) ).
tff(thm_2Esptree_2Elookup__inter,axiom,
! [A_27a: $tType,A_27b: $tType,F2_2E0: tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a))),F1_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),F0_2E0: tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a)))] :
( ! [V5v_2E0: A_27a,V6w_2E0: A_27b] : ( app_2E2(A_27b,tyop_2Eoption_2Eoption(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),F2_2E0,V5v_2E0),V6w_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V5v_2E0) )
=> ( ! [V4v4_2E0: tyop_2Eoption_2Eoption(A_27b),V5v_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),F1_2E0,V4v4_2E0),V5v_2E0) = c_2Eoption_2Eoption__CASE_2E3(A_27b,tyop_2Eoption_2Eoption(A_27a),V4v4_2E0,c_2Eoption_2ENONE_2E0(A_27a),app_2E2(A_27a,tyop_2Emin_2Efun(A_27b,tyop_2Eoption_2Eoption(A_27a)),F2_2E0,V5v_2E0)) )
=> ( ! [V3v3_2E0: tyop_2Eoption_2Eoption(A_27a),V4v4_2E0: tyop_2Eoption_2Eoption(A_27b)] : ( app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Emin_2Efun(tyop_2Eoption_2Eoption(A_27b),tyop_2Eoption_2Eoption(A_27a)),F0_2E0,V3v3_2E0),V4v4_2E0) = c_2Eoption_2Eoption__CASE_2E3(A_27a,tyop_2Eoption_2Eoption(A_27a),V3v3_2E0,c_2Eoption_2ENONE_2E0(A_27a),app_2E2(tyop_2Eoption_2Eoption(A_27b),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),F1_2E0,V4v4_2E0)) )
=> ! [V0m1_2E0: tyop_2Esptree_2Espt(A_27a),V1m2_2E0: tyop_2Esptree_2Espt(A_27b),V2k_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Elookup_2E2(A_27a,V2k_2E0,c_2Esptree_2Einter_2E2(A_27a,A_27b,V0m1_2E0,V1m2_2E0)) = c_2Epair_2Epair__CASE_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b),c_2Epair_2E_2C_2E2(tyop_2Eoption_2Eoption(A_27a),tyop_2Eoption_2Eoption(A_27b),c_2Esptree_2Elookup_2E2(A_27a,V2k_2E0,V0m1_2E0),c_2Esptree_2Elookup_2E2(A_27b,V2k_2E0,V1m2_2E0)),F0_2E0) ) ) ) ) ).
tff(thm_2Esptree_2Elookup__inter__eq,axiom,
! [A_27a: $tType,F1_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool))),F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))))] :
( ! [V2k_2E0: tyop_2Enum_2Enum,V1m2_2E0: tyop_2Esptree_2Espt(A_27a),V3v_2E0: A_27a] :
( p(app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V2k_2E0),V1m2_2E0),V3v_2E0))
<=> ( c_2Esptree_2Elookup_2E2(A_27a,V2k_2E0,V1m2_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V3v_2E0) ) )
=> ( ! [V2k_2E0: tyop_2Enum_2Enum,V1m2_2E0: tyop_2Esptree_2Espt(A_27a),V3v_2E0: A_27a] : ( app_2E2(A_27a,tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),F0_2E0,V2k_2E0),V1m2_2E0),V3v_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),app_2E2(A_27a,tyop_2Emin_2Ebool,app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Emin_2Ebool)),F1_2E0,V2k_2E0),V1m2_2E0),V3v_2E0),c_2Eoption_2ESOME_2E1(A_27a,V3v_2E0),c_2Eoption_2ENONE_2E0(A_27a)) )
=> ! [V0m1_2E0: tyop_2Esptree_2Espt(A_27a),V1m2_2E0: tyop_2Esptree_2Espt(A_27a),V2k_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Elookup_2E2(A_27a,V2k_2E0,c_2Esptree_2Einter__eq_2E2(A_27a,V0m1_2E0,V1m2_2E0)) = c_2Eoption_2Eoption__CASE_2E3(A_27a,tyop_2Eoption_2Eoption(A_27a),c_2Esptree_2Elookup_2E2(A_27a,V2k_2E0,V0m1_2E0),c_2Eoption_2ENONE_2E0(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a)),app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27a),tyop_2Emin_2Efun(A_27a,tyop_2Eoption_2Eoption(A_27a))),F0_2E0,V2k_2E0),V1m2_2E0)) ) ) ) ).
tff(thm_2Esptree_2Elookup__inter__EQ,axiom,
! [A_27a: $tType,A_27b: $tType,V0y_2E0: A_27a,V1x_2E0: tyop_2Enum_2Enum,V2t2_2E0: tyop_2Esptree_2Espt(A_27b),V3t1_2E0: tyop_2Esptree_2Espt(A_27a)] :
( ( ( c_2Esptree_2Elookup_2E2(A_27a,V1x_2E0,c_2Esptree_2Einter_2E2(A_27a,A_27b,V3t1_2E0,V2t2_2E0)) = c_2Eoption_2ESOME_2E1(A_27a,V0y_2E0) )
<=> ( ( c_2Esptree_2Elookup_2E2(A_27a,V1x_2E0,V3t1_2E0) = c_2Eoption_2ESOME_2E1(A_27a,V0y_2E0) )
& ( c_2Esptree_2Elookup_2E2(A_27b,V1x_2E0,V2t2_2E0) != c_2Eoption_2ENONE_2E0(A_27b) ) ) )
& ( ( c_2Esptree_2Elookup_2E2(A_27a,V1x_2E0,c_2Esptree_2Einter_2E2(A_27a,A_27b,V3t1_2E0,V2t2_2E0)) = c_2Eoption_2ENONE_2E0(A_27a) )
<=> ( ( c_2Esptree_2Elookup_2E2(A_27a,V1x_2E0,V3t1_2E0) = c_2Eoption_2ENONE_2E0(A_27a) )
| ( c_2Esptree_2Elookup_2E2(A_27b,V1x_2E0,V2t2_2E0) = c_2Eoption_2ENONE_2E0(A_27b) ) ) ) ) ).
tff(thm_2Esptree_2Elookup__inter__assoc,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0x_2E0: tyop_2Enum_2Enum,V1t3_2E0: tyop_2Esptree_2Espt(A_27c),V2t2_2E0: tyop_2Esptree_2Espt(A_27b),V3t1_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Elookup_2E2(A_27a,V0x_2E0,c_2Esptree_2Einter_2E2(A_27a,A_27b,V3t1_2E0,c_2Esptree_2Einter_2E2(A_27b,A_27c,V2t2_2E0,V1t3_2E0))) = c_2Esptree_2Elookup_2E2(A_27a,V0x_2E0,c_2Esptree_2Einter_2E2(A_27a,A_27c,c_2Esptree_2Einter_2E2(A_27a,A_27b,V3t1_2E0,V2t2_2E0),V1t3_2E0)) ) ).
tff(thm_2Esptree_2Elookup__difference,axiom,
! [A_27a: $tType,A_27b: $tType,F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Ebool))] :
( ! [V2k_2E0: tyop_2Enum_2Enum,V1m2_2E0: tyop_2Esptree_2Espt(A_27b)] :
( p(app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Ebool),F0_2E0,V2k_2E0),V1m2_2E0))
<=> ( c_2Esptree_2Elookup_2E2(A_27b,V2k_2E0,V1m2_2E0) = c_2Eoption_2ENONE_2E0(A_27b) ) )
=> ! [V0m1_2E0: tyop_2Esptree_2Espt(A_27a),V1m2_2E0: tyop_2Esptree_2Espt(A_27b),V2k_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Elookup_2E2(A_27a,V2k_2E0,c_2Esptree_2Edifference_2E2(A_27a,A_27b,V0m1_2E0,V1m2_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27a),app_2E2(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Ebool,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Efun(tyop_2Esptree_2Espt(A_27b),tyop_2Emin_2Ebool),F0_2E0,V2k_2E0),V1m2_2E0),c_2Esptree_2Elookup_2E2(A_27a,V2k_2E0,V0m1_2E0),c_2Eoption_2ENONE_2E0(A_27a)) ) ) ).
tff(thm_2Esptree_2Elrnext__ind,axiom,
! [V0P_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( ! [V1n_2E0: tyop_2Enum_2Enum] :
( ( ( V1n_2E0 != c_2Enum_2E0_2E0 )
=> p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V1n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))))) )
=> p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,V1n_2E0)) )
=> ! [V2v_2E0: tyop_2Enum_2Enum] : p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,V0P_2E0,V2v_2E0)) ) ).
tff(thm_2Esptree_2Elrnext__def,axiom,
! [F0_2E0: tyop_2Emin_2Efun(tyop_2Enum_2Enum,tyop_2Emin_2Ebool)] :
( ! [V0n_2E0: tyop_2Enum_2Enum] :
( p(app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V0n_2E0))
<=> ( V0n_2E0 = c_2Enum_2E0_2E0 ) )
=> ! [V0n_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Elrnext_2E1(V0n_2E0) = c_2Ebool_2ECOND_2E3(tyop_2Enum_2Enum,app_2E2(tyop_2Enum_2Enum,tyop_2Emin_2Ebool,F0_2E0,V0n_2E0),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Esptree_2Elrnext_2E1(c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V0n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)))))) ) ) ).
tff(thm_2Esptree_2Elrnext__thm,axiom,
! [A_27a: $tType,A_27b: $tType] :
( ! [V0a_2E0: A_27a] : ( c_2Esptree_2Elrnext_2E1(c_2Enum_2E0_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) )
& ! [V1n_2E0: tyop_2Enum_2Enum,V2a_2E0: A_27b] : ( c_2Esptree_2Elrnext_2E1(c_2Earithmetic_2ENUMERAL_2E1(V1n_2E0)) = c_2Esptree_2Elrnext_2E1(V1n_2E0) )
& ( c_2Esptree_2Elrnext_2E1(c_2Earithmetic_2EZERO_2E0) = c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0)) )
& ! [V3n_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Elrnext_2E1(c_2Earithmetic_2EBIT1_2E1(V3n_2E0)) = c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Esptree_2Elrnext_2E1(V3n_2E0)) )
& ! [V4n_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Elrnext_2E1(c_2Earithmetic_2EBIT2_2E1(V4n_2E0)) = c_2Earithmetic_2E_2A_2E2(c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0)),c_2Esptree_2Elrnext_2E1(V4n_2E0)) ) ) ).
tff(thm_2Esptree_2EFINITE__domain,axiom,
! [A_27a: $tType,V0t_2E0: tyop_2Esptree_2Espt(A_27a)] : p(c_2Epred__set_2EFINITE_2E1(tyop_2Enum_2Enum,c_2Esptree_2Edomain_2E1(A_27a,V0t_2E0))) ).
tff(thm_2Esptree_2EIN__domain,axiom,
! [A_27a: $tType,A_27b: $tType,V0n_2E0: tyop_2Enum_2Enum,V1x_2E0: A_27a,V2t1_2E0: tyop_2Esptree_2Espt(A_27a),V3t2_2E0: tyop_2Esptree_2Espt(A_27a)] :
( ( c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V0n_2E0,c_2Esptree_2Edomain_2E1(A_27b,c_2Esptree_2ELN_2E0(A_27b))) = c_2Ebool_2EF_2E0 )
& ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V0n_2E0,c_2Esptree_2Edomain_2E1(A_27a,c_2Esptree_2ELS_2E1(A_27a,V1x_2E0))))
<=> ( V0n_2E0 = c_2Enum_2E0_2E0 ) )
& ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V0n_2E0,c_2Esptree_2Edomain_2E1(A_27a,c_2Esptree_2EBN_2E2(A_27a,V2t1_2E0,V3t2_2E0))))
<=> ( ( V0n_2E0 != c_2Enum_2E0_2E0 )
& p(c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(V0n_2E0),c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V0n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Esptree_2Edomain_2E1(A_27a,V2t1_2E0)),c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V0n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Esptree_2Edomain_2E1(A_27a,V3t2_2E0)))) ) )
& ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V0n_2E0,c_2Esptree_2Edomain_2E1(A_27a,c_2Esptree_2EBS_2E3(A_27a,V2t1_2E0,V1x_2E0,V3t2_2E0))))
<=> ( ( V0n_2E0 = c_2Enum_2E0_2E0 )
| p(c_2Ebool_2ECOND_2E3(tyop_2Emin_2Ebool,c_2Earithmetic_2EEVEN_2E1(V0n_2E0),c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V0n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Esptree_2Edomain_2E1(A_27a,V2t1_2E0)),c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,c_2Earithmetic_2EDIV_2E2(c_2Earithmetic_2E_2D_2E2(V0n_2E0,c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT1_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Earithmetic_2ENUMERAL_2E1(c_2Earithmetic_2EBIT2_2E1(c_2Earithmetic_2EZERO_2E0))),c_2Esptree_2Edomain_2E1(A_27a,V3t2_2E0)))) ) ) ) ).
tff(thm_2Esptree_2Emap__map__K,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0f_2E0: tyop_2Emin_2Efun(A_27a,A_27c),V1a_2E0: A_27b,V2t_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Emap_2E2(A_27b,A_27c,c_2Ecombin_2EK_2E1(A_27b,A_27c,V1a_2E0),c_2Esptree_2Emap_2E2(A_27c,A_27a,V0f_2E0,V2t_2E0)) = c_2Esptree_2Emap_2E2(A_27b,A_27a,c_2Ecombin_2EK_2E1(A_27b,A_27a,V1a_2E0),V2t_2E0) ) ).
tff(thm_2Esptree_2Elookup__map__K,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: A_27b,V1t_2E0: tyop_2Esptree_2Espt(A_27a),V2n_2E0: tyop_2Enum_2Enum] : ( c_2Esptree_2Elookup_2E2(A_27b,V2n_2E0,c_2Esptree_2Emap_2E2(A_27b,A_27a,c_2Ecombin_2EK_2E1(A_27b,A_27a,V0x_2E0),V1t_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(A_27b),c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V2n_2E0,c_2Esptree_2Edomain_2E1(A_27a,V1t_2E0)),c_2Eoption_2ESOME_2E1(A_27b,V0x_2E0),c_2Eoption_2ENONE_2E0(A_27b)) ) ).
tff(thm_2Esptree_2EIMP__size__LESS__size,axiom,
! [A_27a: $tType,V0x_2E0: tyop_2Esptree_2Espt(A_27a),V1y_2E0: tyop_2Esptree_2Espt(A_27a)] :
( ( p(c_2Esptree_2Esubspt_2E2(A_27a,V0x_2E0,V1y_2E0))
& ( c_2Esptree_2Edomain_2E1(A_27a,V0x_2E0) != c_2Esptree_2Edomain_2E1(A_27a,V1y_2E0) ) )
=> p(c_2Eprim__rec_2E_3C_2E2(c_2Esptree_2Esize_2E1(A_27a,V0x_2E0),c_2Esptree_2Esize_2E1(A_27a,V1y_2E0))) ) ).
tff(thm_2Esptree_2Esize__diff__less,axiom,
! [A_27a: $tType,A_27b: $tType,A_27c: $tType,V0x_2E0: tyop_2Esptree_2Espt(A_27a),V1y_2E0: tyop_2Esptree_2Espt(A_27b),V2z_2E0: tyop_2Esptree_2Espt(A_27c),V3t_2E0: tyop_2Enum_2Enum] :
( ( p(c_2Epred__set_2ESUBSET_2E2(tyop_2Enum_2Enum,c_2Esptree_2Edomain_2E1(A_27c,V2z_2E0),c_2Esptree_2Edomain_2E1(A_27b,V1y_2E0)))
& p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V3t_2E0,c_2Esptree_2Edomain_2E1(A_27b,V1y_2E0)))
& ~ p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V3t_2E0,c_2Esptree_2Edomain_2E1(A_27c,V2z_2E0)))
& p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V3t_2E0,c_2Esptree_2Edomain_2E1(A_27a,V0x_2E0))) )
=> p(c_2Eprim__rec_2E_3C_2E2(c_2Esptree_2Esize_2E1(A_27a,c_2Esptree_2Edifference_2E2(A_27a,A_27b,V0x_2E0,V1y_2E0)),c_2Esptree_2Esize_2E1(A_27a,c_2Esptree_2Edifference_2E2(A_27a,A_27c,V0x_2E0,V2z_2E0)))) ) ).
tff(thm_2Esptree_2Einter__eq__LN,axiom,
! [A_27a: $tType,A_27b: $tType,V0x_2E0: tyop_2Esptree_2Espt(A_27a),V1y_2E0: tyop_2Esptree_2Espt(A_27b)] :
( ( c_2Esptree_2Einter_2E2(A_27a,A_27b,V0x_2E0,V1y_2E0) = c_2Esptree_2ELN_2E0(A_27a) )
<=> p(c_2Epred__set_2EDISJOINT_2E2(tyop_2Enum_2Enum,c_2Esptree_2Edomain_2E1(A_27a,V0x_2E0),c_2Esptree_2Edomain_2E1(A_27b,V1y_2E0))) ) ).
tff(thm_2Esptree_2Edomain__list__to__num__set,axiom,
! [V0x_2E0: tyop_2Enum_2Enum,V1xs_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V0x_2E0,c_2Esptree_2Edomain_2E1(tyop_2Eone_2Eone,c_2Esptree_2Elist__to__num__set_2E1(V1xs_2E0))) = c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V0x_2E0,c_2Elist_2ELIST__TO__SET_2E1(tyop_2Enum_2Enum,V1xs_2E0)) ) ).
tff(thm_2Esptree_2Edomain__list__insert,axiom,
! [V0xs_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum),V1x_2E0: tyop_2Enum_2Enum,V2t_2E0: tyop_2Esptree_2Espt(tyop_2Eone_2Eone)] :
( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V1x_2E0,c_2Esptree_2Edomain_2E1(tyop_2Eone_2Eone,c_2Esptree_2Elist__insert_2E2(V0xs_2E0,V2t_2E0))))
<=> ( p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V1x_2E0,c_2Elist_2ELIST__TO__SET_2E1(tyop_2Enum_2Enum,V0xs_2E0)))
| p(c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V1x_2E0,c_2Esptree_2Edomain_2E1(tyop_2Eone_2Eone,V2t_2E0))) ) ) ).
tff(thm_2Esptree_2Edomain__FOLDR__delete,axiom,
! [A_27a: $tType,V0ls_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum),V1live_2E0: tyop_2Esptree_2Espt(A_27a)] : ( c_2Esptree_2Edomain_2E1(A_27a,c_2Elist_2EFOLDR_2E3(tyop_2Enum_2Enum,tyop_2Esptree_2Espt(A_27a),c_2Esptree_2Edelete_2E0(A_27a),V1live_2E0,V0ls_2E0)) = c_2Epred__set_2EDIFF_2E2(tyop_2Enum_2Enum,c_2Esptree_2Edomain_2E1(A_27a,V1live_2E0),c_2Elist_2ELIST__TO__SET_2E1(tyop_2Enum_2Enum,V0ls_2E0)) ) ).
tff(thm_2Esptree_2Elookup__list__to__num__set,axiom,
! [V0x_2E0: tyop_2Enum_2Enum,V1xs_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Esptree_2Elookup_2E2(tyop_2Eone_2Eone,V0x_2E0,c_2Esptree_2Elist__to__num__set_2E1(V1xs_2E0)) = c_2Ebool_2ECOND_2E3(tyop_2Eoption_2Eoption(tyop_2Eone_2Eone),c_2Ebool_2EIN_2E2(tyop_2Enum_2Enum,V0x_2E0,c_2Elist_2ELIST__TO__SET_2E1(tyop_2Enum_2Enum,V1xs_2E0)),c_2Eoption_2ESOME_2E1(tyop_2Eone_2Eone,c_2Eone_2Eone_2E0),c_2Eoption_2ENONE_2E0(tyop_2Eone_2Eone)) ) ).
tff(thm_2Esptree_2Elist__to__num__set__append,axiom,
! [V0l1_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum),V1l2_2E0: tyop_2Elist_2Elist(tyop_2Enum_2Enum)] : ( c_2Esptree_2Elist__to__num__set_2E1(c_2Elist_2EAPPEND_2E2(tyop_2Enum_2Enum,V0l1_2E0,V1l2_2E0)) = c_2Esptree_2Eunion_2E2(tyop_2Eone_2Eone,c_2Esptree_2Elist__to__num__set_2E1(V0l1_2E0),c_2Esptree_2Elist__to__num__set_2E1(V1l2_2E0)) ) ).
%------------------------------------------------------------------------------